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Franc ¸ois Loret 2
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
NIKOLAOS BOURNAVEAS AND GEORGIOS E. ZOURARIS ESAIM: M2AN 46 (2012) 841–874 ESAIM: Mathematical Modelling and Numerical Analysis DOI: 10.1051/m2an/2011071 www.esaim-m2an.org THEORY AND NUMERICAL APPROXIMATIONS FOR A NONLINEAR 1 + 1 DIRAC SYSTEM Nikolaos Bournaveas1 and Georgios E. Zouraris2 Abstract. APPROXIMATION PROPERTIES OF PERIODIC INTERPOLATION BY APPROXIMATION PROPERTIES OF PERIODIC INTERPOLATION 181 Fourier partial sum projector F n is defined by m Fn(f)= £ (f,ek)ek (m= ). k=~m Clearly, Fn is a bounded linear operator on ^2 TT * On the other hand, it is well known that the norms ||Frt||, n G M, are not uniformly bounded.According to the Banach Steinhaus principle , Fn(f ), n e N, is not convergent for A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. A MODAL SYNTHESIS METHOD FOR THE ELASTOACOUSTIC VIBRATION A MODAL SYNTHESIS METHOD FOR THE ELASTOACOUSTIC VIBRATION PROBLEM 125 Theorem 2.1. The set of eigenvalues of VP consists of a sequence of positive real numbers converging to +1. All of them have nite multiplicity and their ascent is one. THE SINGULARITY EXPANSION METHOD APPLIED TO THE TRANSIENT ESAIM: M2AN ESAIM: Mathematical Modelling and Numerical Analysis Vol. 41, N o 5, 2007, pp. 925 943 www.esaim-m2an.org DOI: 10.1051/m2an:2007040 THE SINGULARITY EXPANSION METHOD APPLIED TO THE TRANSIENT MOTIONS OF A FLOATING ELASTIC PLATE Christophe Hazard 1 andFranc ¸ois Loret 2
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
NIKOLAOS BOURNAVEAS AND GEORGIOS E. ZOURARIS ESAIM: M2AN 46 (2012) 841–874 ESAIM: Mathematical Modelling and Numerical Analysis DOI: 10.1051/m2an/2011071 www.esaim-m2an.org THEORY AND NUMERICAL APPROXIMATIONS FOR A NONLINEAR 1 + 1 DIRAC SYSTEM Nikolaos Bournaveas1 and Georgios E. Zouraris2 Abstract. APPROXIMATION PROPERTIES OF PERIODIC INTERPOLATION BY APPROXIMATION PROPERTIES OF PERIODIC INTERPOLATION 181 Fourier partial sum projector F n is defined by m Fn(f)= £ (f,ek)ek (m= ). k=~m Clearly, Fn is a bounded linear operator on ^2 TT * On the other hand, it is well known that the norms ||Frt||, n G M, are not uniformly bounded.According to the Banach Steinhaus principle , Fn(f ), n e N, is not convergent for A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we THE SINGULARITY EXPANSION METHOD APPLIED TO THE TRANSIENT ESAIM: M2AN ESAIM: Mathematical Modelling and Numerical Analysis Vol. 41, N o 5, 2007, pp. 925 943 www.esaim-m2an.org DOI: 10.1051/m2an:2007040 THE SINGULARITY EXPANSION METHOD APPLIED TO THE TRANSIENT MOTIONS OF A FLOATING ELASTIC PLATE Christophe Hazard 1 and Franc ¸ois Loret 2 Abstract. NIKOLAOS BOURNAVEAS AND GEORGIOS E. ZOURARIS ESAIM: M2AN 46 (2012) 841–874 ESAIM: Mathematical Modelling and Numerical Analysis DOI: 10.1051/m2an/2011071 www.esaim-m2an.org THEORY AND NUMERICAL APPROXIMATIONS FOR A NONLINEAR 1 + 1 DIRAC SYSTEM Nikolaos Bournaveas1 and Georgios E. Zouraris2 Abstract. APPROXIMATION PROPERTIES OF PERIODIC INTERPOLATION BY APPROXIMATION PROPERTIES OF PERIODIC INTERPOLATION 181 Fourier partial sum projector F n is defined by m Fn(f)= £ (f,ek)ek (m= ). k=~m Clearly, Fn is a bounded linear operator on ^2 TT * On the other hand, it is well known that the norms ||Frt||, n G M, are not uniformly bounded.According to the Banach Steinhaus principle , Fn(f ), n e N, is not convergent for SEMI–SMOOTH NEWTON METHODS FOR VARIATIONAL … 44 K. ITO AND K. KUNISCH Let us consider Newton–differentiability of the max–operator. For this purpose X denotes a function space of real–valued functions on Ω ⊂ Rn and max(0,y) is the pointwise max–operation.For δ ∈ R we introduce candidates for the generalized derivative of the form SHIGE PENG AND MINGYU XU 336 S. PENG AND M. XU The solution of a BSDE is a couple of progressive measurable processes (Y,Z), which satisfiesY t = ξ + T t g(s,Y s,Z s)ds− T t Z sdB s, (1.1) where B is a Brownian motion. Here ξ is terminal condition and g is a generator. From , we know that when ξ is a square integrable random variable, and g satisfies Lipschitz condition and some integrability TIME DISCRETIZATION OF PARABOLIC PROBLEMS BY THE mathematlcalmooeujhganohumericalanalysts mooÉusat1on mathÉmatique et analyse numÉrique (vol. 19, nû 4,1985, p. 611 à 643) time discretization of parabolic CONFORMING AND NONCONFORMING FINITE ELEMENT METHODS FOR METHODS FOR SOLVING THE STATIONARY STOKES EQUATIONS 37 In order to approximate problems (2.13) or (2.15), we first construct a triangulation T5fc of the set Q with nondegenerate JV-simplices i£(i.e. triangles if N = 2 or tetrahedrons if N = 3) with diameters <h.
CENTRAL WENO SCHEMES FOR HYPERBOLIC SYSTEMS OF Mathematical Modelling and Numerical Analysis M2AN, Vol. 33, No 3, 1999, p. 547{571 Mod elisation Math ematique et Analyse Num erique CENTRAL WENO SCHEMES FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS FINITE VOLUMES AND NONLINEAR DIFFUSION EQUATIONS 750 R. EYMARD, T. GALLOUËT, D. HILHORST and Y. NAÏT SLIMANE Vp = km( ) \ v(x 9t)dxdt, for all/? e gr, forallneM(10) . (iii) The explicit finite volume scheme is defined by i vn for allp e 2T, for all n e fcl , (11) qeN(p) where we set (ppK = (p(un p), for all p e ST and n e N. Equation (11) formally corresponds to integrating the équation (1) on the element px(nk, (n+l)k) and defining a ON FINDING THE LARGEST ROOT OF A POLYNOMIAL _ modelung and numer1gal analys1s mathÉmatique et analyse numÉrique (vol 24, n° 6, 1990, p. 693 à 696) on finding the largest root of apolynomial (*)
A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL124 A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. SEMI–SMOOTH NEWTON METHODS FOR VARIATIONAL … 44 K. ITO AND K. KUNISCH Let us consider Newton–differentiability of the max–operator. For this purpose X denotes a function space of real–valued functions on Ω ⊂ Rn and max(0,y) is the pointwise max–operation.For δ ∈ R we introduce candidates for the generalized derivative of the form THE SINGULARITY EXPANSION METHOD APPLIED TO THE TRANSIENT ESAIM: M2AN ESAIM: Mathematical Modelling and Numerical Analysis Vol. 41, N o 5, 2007, pp. 925 943 www.esaim-m2an.org DOI: 10.1051/m2an:2007040 THE SINGULARITY EXPANSION METHOD APPLIED TO THE TRANSIENT MOTIONS OF A FLOATING ELASTIC PLATE Christophe Hazard 1 andFranc ¸ois Loret 2
GALERKIN TIME-STEPPING METHODS FOR NONLINEAR … GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS 263 in a tube T u,T u:= {v ∈ V:min t u(t)−v≤ 1}, around the solutionu, uniformly in t, with a constant λ¯ less than one. It is easily seen that (1.4) can be written in the form of a G˚arding-typeinequality,
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
APPROXIMATION PROPERTIES OF PERIODIC INTERPOLATION BY APPROXIMATION PROPERTIES OF PERIODIC INTERPOLATION 181 Fourier partial sum projector F n is defined by m Fn(f)= £ (f,ek)ek (m= ). k=~m Clearly, Fn is a bounded linear operator on ^2 TT * On the other hand, it is well known that the norms ||Frt||, n G M, are not uniformly bounded.According to the Banach Steinhaus principle , Fn(f ), n e N, is not convergent for A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL124 A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. SEMI–SMOOTH NEWTON METHODS FOR VARIATIONAL … 44 K. ITO AND K. KUNISCH Let us consider Newton–differentiability of the max–operator. For this purpose X denotes a function space of real–valued functions on Ω ⊂ Rn and max(0,y) is the pointwise max–operation.For δ ∈ R we introduce candidates for the generalized derivative of the form THE SINGULARITY EXPANSION METHOD APPLIED TO THE TRANSIENT ESAIM: M2AN ESAIM: Mathematical Modelling and Numerical Analysis Vol. 41, N o 5, 2007, pp. 925 943 www.esaim-m2an.org DOI: 10.1051/m2an:2007040 THE SINGULARITY EXPANSION METHOD APPLIED TO THE TRANSIENT MOTIONS OF A FLOATING ELASTIC PLATE Christophe Hazard 1 andFranc ¸ois Loret 2
GALERKIN TIME-STEPPING METHODS FOR NONLINEAR … GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS 263 in a tube T u,T u:= {v ∈ V:min t u(t)−v≤ 1}, around the solutionu, uniformly in t, with a constant λ¯ less than one. It is easily seen that (1.4) can be written in the form of a G˚arding-typeinequality,
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
APPROXIMATION PROPERTIES OF PERIODIC INTERPOLATION BY APPROXIMATION PROPERTIES OF PERIODIC INTERPOLATION 181 Fourier partial sum projector F n is defined by m Fn(f)= £ (f,ek)ek (m= ). k=~m Clearly, Fn is a bounded linear operator on ^2 TT * On the other hand, it is well known that the norms ||Frt||, n G M, are not uniformly bounded.According to the Banach Steinhaus principle , Fn(f ), n e N, is not convergent for A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract RECEIVED SEPTEMBER 25, 2020. ACCEPTED JANUARY 26, 2021. A NON-LOCAL MACROSCOPIC MODEL FOR TRAFFIC FLOW 691 for some 𝜀>0 and where 0 is a Lipschitz continuous function (we denote by 0 its Lipschitz constant). From a tra c point of view, we also assume that 0 is non-decreasing. Then, if we de ne 𝜀by 𝜀( , ) := 𝜀 ⌊ 𝜀 ESAIM: MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS Raphaèle Herbin Université d'Aix-Marseille France Website Raphaèle Herbin is a French mathematician, specialist in the numerical analysis of partial differential equations, Professor at the University of Aix-Marseille and member of the Institute of Mathematics of Marseille. PATRIK KNOPF , KEI FONG LAM , CHUN LIU PHASE-FIELD DYNAMICS WITH TRANSFER OF MATERIALS 231 Here ∇ Γ denotes the surface gradient on , is a surface potential, is a non-negative parameter acting as a weight for surface di usion e ects and >0 is related to the thickness of the interfacial regions on theboundary.
SHIGE PENG AND MINGYU XU 336 S. PENG AND M. XU The solution of a BSDE is a couple of progressive measurable processes (Y,Z), which satisfiesY t = ξ + T t g(s,Y s,Z s)ds− T t Z sdB s, (1.1) where B is a Brownian motion. Here ξ is terminal condition and g is a generator. From , we know that when ξ is a square integrable random variable, and g satisfies Lipschitz condition and some integrability SEMI–SMOOTH NEWTON METHODS FOR VARIATIONAL … 44 K. ITO AND K. KUNISCH Let us consider Newton–differentiability of the max–operator. For this purpose X denotes a function space of real–valued functions on Ω ⊂ Rn and max(0,y) is the pointwise max–operation.For δ ∈ R we introduce candidates for the generalized derivative of the form CONFORMING AND NONCONFORMING FINITE ELEMENT METHODS FOR METHODS FOR SOLVING THE STATIONARY STOKES EQUATIONS 37 In order to approximate problems (2.13) or (2.15), we first construct a triangulation T5fc of the set Q with nondegenerate JV-simplices i£(i.e. triangles if N = 2 or tetrahedrons if N = 3) with diameters <h.
'OPTIMISATION PAR RELAXATION R.A.I.R.O. (7e année, décembre 1973, R-3, p. 5 à 32) SUR DES METHODES D'OPTIMISATION PAR RELAXATION par J. CEA (*) et R. GLOWINSKI (2)Communiqué par J. CEA Résumé. Dans cet article, les auteurs étudient les méthodes de relaxation, sousj sur relaxation FINITE VOLUMES AND NONLINEAR DIFFUSION EQUATIONS 750 R. EYMARD, T. GALLOUËT, D. HILHORST and Y. NAÏT SLIMANE Vp = km( ) \ v(x 9t)dxdt, for all/? e gr, forallneM(10) . (iii) The explicit finite volume scheme is defined by i vn for allp e 2T, for all n e fcl , (11) qeN(p) where we set (ppK = (p(un p), for all p e ST and n e N. Equation (11) formally corresponds to integrating the équation (1) on the element px(nk, (n+l)k) and defining a UNE MÉTHODE VARIATIONNELLE D’ÉLÉMENTS FINIS POUR LA r.axr.o. (7* année, décembre 1973, r-3, p. 105 à 129) une methode variationnelle d'elements finis pour la resolution numerique d'un probleme exterieur dans r3 par j.-c. nedelec (*) et j. planchard (2)communiqué par p. g. ciarlet résumé. ON FINDING THE LARGEST ROOT OF A POLYNOMIAL _ modelung and numer1gal analys1s mathÉmatique et analyse numÉrique (vol 24, n° 6, 1990, p. 693 à 696) on finding the largest root of apolynomial (*)
A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL124 A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. AN ANALYSIS OF THE SCHARFETTER-GUMMEL BOX METHOD FOR THE SEMICONDUCTOR DEVICE EQUATIONS 127 where Th dénotes a triangulation of O with each triangle t having diameter less than or equal to h and h0 is a positive constant which is smaller than the diameter of H. For each Th e TS, let Xh = {x,}^ dénote the vertices of Th and Eh = {et}^ the edges of Th.We assume that the nodes in Xh and the edges in Eh are numbered such thatX^ = {*;}^ and E'h = {et}^ GALERKIN TIME-STEPPING METHODS FOR NONLINEAR … GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS 263 in a tube T u,T u:= {v ∈ V:min t u(t)−v≤ 1}, around the solutionu, uniformly in t, with a constant λ¯ less than one. It is easily seen that (1.4) can be written in the form of a G˚arding-typeinequality,
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
SHIGE PENG AND MINGYU XU 336 S. PENG AND M. XU The solution of a BSDE is a couple of progressive measurable processes (Y,Z), which satisfiesY t = ξ + T t g(s,Y s,Z s)ds− T t Z sdB s, (1.1) where B is a Brownian motion. Here ξ is terminal condition and g is a generator. From , we know that when ξ is a square integrable random variable, and g satisfies Lipschitz condition and some integrability ANALYSIS AND FINITE ELEMENT APPROXIMATION OF OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS 715 and For functions defïned on Fc we will use the subspaces Hj(rc) if Fc has a boundary and where Hj(rc)= Hj(Fc) otherwise JHJ(FC) O Hj(F c) if F has a boundary otherwise , g.ndT = and, whenever Fc has a boundary, Hj(rc)= {geH 1(r c)|g = o onarc}. Norms of functions belonging to ^J(fi), ^(F) and HS(T C) are denoted by A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL124 A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. AN ANALYSIS OF THE SCHARFETTER-GUMMEL BOX METHOD FOR THE SEMICONDUCTOR DEVICE EQUATIONS 127 where Th dénotes a triangulation of O with each triangle t having diameter less than or equal to h and h0 is a positive constant which is smaller than the diameter of H. For each Th e TS, let Xh = {x,}^ dénote the vertices of Th and Eh = {et}^ the edges of Th.We assume that the nodes in Xh and the edges in Eh are numbered such thatX^ = {*;}^ and E'h = {et}^ GALERKIN TIME-STEPPING METHODS FOR NONLINEAR … GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS 263 in a tube T u,T u:= {v ∈ V:min t u(t)−v≤ 1}, around the solutionu, uniformly in t, with a constant λ¯ less than one. It is easily seen that (1.4) can be written in the form of a G˚arding-typeinequality,
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
SHIGE PENG AND MINGYU XU 336 S. PENG AND M. XU The solution of a BSDE is a couple of progressive measurable processes (Y,Z), which satisfiesY t = ξ + T t g(s,Y s,Z s)ds− T t Z sdB s, (1.1) where B is a Brownian motion. Here ξ is terminal condition and g is a generator. From , we know that when ξ is a square integrable random variable, and g satisfies Lipschitz condition and some integrability ANALYSIS AND FINITE ELEMENT APPROXIMATION OF OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS 715 and For functions defïned on Fc we will use the subspaces Hj(rc) if Fc has a boundary and where Hj(rc)= Hj(Fc) otherwise JHJ(FC) O Hj(F c) if F has a boundary otherwise , g.ndT = and, whenever Fc has a boundary, Hj(rc)= {geH 1(r c)|g = o onarc}. Norms of functions belonging to ^J(fi), ^(F) and HS(T C) are denoted by A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of CONFORMING AND NONCONFORMING FINITE ELEMENT METHODS FOR METHODS FOR SOLVING THE STATIONARY STOKES EQUATIONS 37 In order to approximate problems (2.13) or (2.15), we first construct a triangulation T5fc of the set Q with nondegenerate JV-simplices i£(i.e. triangles if N = 2 or tetrahedrons if N = 3) with diameters <h.
SEMI–SMOOTH NEWTON METHODS FOR VARIATIONAL … 44 K. ITO AND K. KUNISCH Let us consider Newton–differentiability of the max–operator. For this purpose X denotes a function space of real–valued functions on Ω ⊂ Rn and max(0,y) is the pointwise max–operation.For δ ∈ R we introduce candidates for the generalized derivative of the form AN ANALYSIS TECHNIQUE FOR STABILIZED FINITE ELEMENT 58 T. CHACON REBOLLO constructed with the mini-element. It is a direct consequence of the fact that this element satis es the discrete inf-sup condition. Such analysis is FINITE ELEMENT APPROXIMATIONS OF THE THREE DIMENSIONAL 982 S.C. BRENNER AND M. NEILAN Remark 2.1. The norms (2.1)–(2.4) are well-defined for functions in W 3, (T h). Let k be an integer greater than or equal to three and define the finite element space V h ⊂ H1(Ω) as follows: • if T ∈T h does not have a curved face, then v T is a polynomial of (total) degree ≤ k in the rectilinear coordinates for T; • if T ∈T h has one curvedC .G.MAKRIDAKIS P
jom matheuatical uodelung and numerical analysis fflmmh modelisation mathematique et analyse numerique (vol 29, n° 2, 1995, p 171 a 197) time-discrete finite element schemes for maxwell's TIME DISCRETIZATION OF PARABOLIC PROBLEMS BY THE mathematlcalmooeujhganohumericalanalysts mooÉusat1on mathÉmatique et analyse numÉrique (vol. 19, nû 4,1985, p. 611 à 643) time discretization of parabolic TOME 19, N 1 (1985), P. 7-32. mathematica!. modbung and numengal analysts modÉlisation mathÉmatique et analyse numÉrique (vol 19, n° 1, 1985, p 7 à 32) mixed and nonconforming finite element methods : APPROXIMATION BY FINITE ELEMENT FUNCTIONS USING LOCAL APPROXIMATION BY UNITE ELEMENT FONCTIONS 79 The functions 7} is bounded by c. H4. For any D 3), all the angles of the T{s are ^ c > 0. ON A CLASS OF IMPLICIT AND EXPLICIT SCHEMES OF VAN-LEER IMPLICIT AND EXPLICIT SCHEMES OF VAN-LEER TYPE 263 for all 4> C°°(K x K+) with compact support in RxR+, and ^ 0, where y\ is the entropy function and F the entropy flux associated with the A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL124 A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. AN ANALYSIS OF THE SCHARFETTER-GUMMEL BOX METHOD FOR THE SEMICONDUCTOR DEVICE EQUATIONS 127 where Th dénotes a triangulation of O with each triangle t having diameter less than or equal to h and h0 is a positive constant which is smaller than the diameter of H. For each Th e TS, let Xh = {x,}^ dénote the vertices of Th and Eh = {et}^ the edges of Th.We assume that the nodes in Xh and the edges in Eh are numbered such thatX^ = {*;}^ and E'h = {et}^ GALERKIN TIME-STEPPING METHODS FOR NONLINEAR … GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS 263 in a tube T u,T u:= {v ∈ V:min t u(t)−v≤ 1}, around the solutionu, uniformly in t, with a constant λ¯ less than one. It is easily seen that (1.4) can be written in the form of a G˚arding-typeinequality,
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
SHIGE PENG AND MINGYU XU 336 S. PENG AND M. XU The solution of a BSDE is a couple of progressive measurable processes (Y,Z), which satisfiesY t = ξ + T t g(s,Y s,Z s)ds− T t Z sdB s, (1.1) where B is a Brownian motion. Here ξ is terminal condition and g is a generator. From , we know that when ξ is a square integrable random variable, and g satisfies Lipschitz condition and some integrability ANALYSIS AND FINITE ELEMENT APPROXIMATION OF OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS 715 and For functions defïned on Fc we will use the subspaces Hj(rc) if Fc has a boundary and where Hj(rc)= Hj(Fc) otherwise JHJ(FC) O Hj(F c) if F has a boundary otherwise , g.ndT = and, whenever Fc has a boundary, Hj(rc)= {geH 1(r c)|g = o onarc}. Norms of functions belonging to ^J(fi), ^(F) and HS(T C) are denoted by A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL124 A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. AN ANALYSIS OF THE SCHARFETTER-GUMMEL BOX METHOD FOR THE SEMICONDUCTOR DEVICE EQUATIONS 127 where Th dénotes a triangulation of O with each triangle t having diameter less than or equal to h and h0 is a positive constant which is smaller than the diameter of H. For each Th e TS, let Xh = {x,}^ dénote the vertices of Th and Eh = {et}^ the edges of Th.We assume that the nodes in Xh and the edges in Eh are numbered such thatX^ = {*;}^ and E'h = {et}^ GALERKIN TIME-STEPPING METHODS FOR NONLINEAR … GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS 263 in a tube T u,T u:= {v ∈ V:min t u(t)−v≤ 1}, around the solutionu, uniformly in t, with a constant λ¯ less than one. It is easily seen that (1.4) can be written in the form of a G˚arding-typeinequality,
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
SHIGE PENG AND MINGYU XU 336 S. PENG AND M. XU The solution of a BSDE is a couple of progressive measurable processes (Y,Z), which satisfiesY t = ξ + T t g(s,Y s,Z s)ds− T t Z sdB s, (1.1) where B is a Brownian motion. Here ξ is terminal condition and g is a generator. From , we know that when ξ is a square integrable random variable, and g satisfies Lipschitz condition and some integrability ANALYSIS AND FINITE ELEMENT APPROXIMATION OF OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS 715 and For functions defïned on Fc we will use the subspaces Hj(rc) if Fc has a boundary and where Hj(rc)= Hj(Fc) otherwise JHJ(FC) O Hj(F c) if F has a boundary otherwise , g.ndT = and, whenever Fc has a boundary, Hj(rc)= {geH 1(r c)|g = o onarc}. Norms of functions belonging to ^J(fi), ^(F) and HS(T C) are denoted by A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of CONFORMING AND NONCONFORMING FINITE ELEMENT METHODS FOR METHODS FOR SOLVING THE STATIONARY STOKES EQUATIONS 37 In order to approximate problems (2.13) or (2.15), we first construct a triangulation T5fc of the set Q with nondegenerate JV-simplices i£(i.e. triangles if N = 2 or tetrahedrons if N = 3) with diameters <h.
SEMI–SMOOTH NEWTON METHODS FOR VARIATIONAL … 44 K. ITO AND K. KUNISCH Let us consider Newton–differentiability of the max–operator. For this purpose X denotes a function space of real–valued functions on Ω ⊂ Rn and max(0,y) is the pointwise max–operation.For δ ∈ R we introduce candidates for the generalized derivative of the form AN ANALYSIS TECHNIQUE FOR STABILIZED FINITE ELEMENT 58 T. CHACON REBOLLO constructed with the mini-element. It is a direct consequence of the fact that this element satis es the discrete inf-sup condition. Such analysis is FINITE ELEMENT APPROXIMATIONS OF THE THREE DIMENSIONAL 982 S.C. BRENNER AND M. NEILAN Remark 2.1. The norms (2.1)–(2.4) are well-defined for functions in W 3, (T h). Let k be an integer greater than or equal to three and define the finite element space V h ⊂ H1(Ω) as follows: • if T ∈T h does not have a curved face, then v T is a polynomial of (total) degree ≤ k in the rectilinear coordinates for T; • if T ∈T h has one curvedC .G.MAKRIDAKIS P
jom matheuatical uodelung and numerical analysis fflmmh modelisation mathematique et analyse numerique (vol 29, n° 2, 1995, p 171 a 197) time-discrete finite element schemes for maxwell's TIME DISCRETIZATION OF PARABOLIC PROBLEMS BY THE mathematlcalmooeujhganohumericalanalysts mooÉusat1on mathÉmatique et analyse numÉrique (vol. 19, nû 4,1985, p. 611 à 643) time discretization of parabolic TOME 19, N 1 (1985), P. 7-32. mathematica!. modbung and numengal analysts modÉlisation mathÉmatique et analyse numÉrique (vol 19, n° 1, 1985, p 7 à 32) mixed and nonconforming finite element methods : APPROXIMATION BY FINITE ELEMENT FUNCTIONS USING LOCAL APPROXIMATION BY UNITE ELEMENT FONCTIONS 79 The functions 7} is bounded by c. H4. For any D 3), all the angles of the T{s are ^ c > 0. ON A CLASS OF IMPLICIT AND EXPLICIT SCHEMES OF VAN-LEER IMPLICIT AND EXPLICIT SCHEMES OF VAN-LEER TYPE 263 for all 4> C°°(K x K+) with compact support in RxR+, and ^ 0, where y\ is the entropy function and F the entropy flux associated with the A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL124 A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. AN ANALYSIS OF THE SCHARFETTER-GUMMEL BOX METHOD FOR THE SEMICONDUCTOR DEVICE EQUATIONS 127 where Th dénotes a triangulation of O with each triangle t having diameter less than or equal to h and h0 is a positive constant which is smaller than the diameter of H. For each Th e TS, let Xh = {x,}^ dénote the vertices of Th and Eh = {et}^ the edges of Th.We assume that the nodes in Xh and the edges in Eh are numbered such thatX^ = {*;}^ and E'h = {et}^ GALERKIN TIME-STEPPING METHODS FOR NONLINEAR … GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS 263 in a tube T u,T u:= {v ∈ V:min t u(t)−v≤ 1}, around the solutionu, uniformly in t, with a constant λ¯ less than one. It is easily seen that (1.4) can be written in the form of a G˚arding-typeinequality,
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
SHIGE PENG AND MINGYU XU 336 S. PENG AND M. XU The solution of a BSDE is a couple of progressive measurable processes (Y,Z), which satisfiesY t = ξ + T t g(s,Y s,Z s)ds− T t Z sdB s, (1.1) where B is a Brownian motion. Here ξ is terminal condition and g is a generator. From , we know that when ξ is a square integrable random variable, and g satisfies Lipschitz condition and some integrability ANALYSIS AND FINITE ELEMENT APPROXIMATION OF OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS 715 and For functions defïned on Fc we will use the subspaces Hj(rc) if Fc has a boundary and where Hj(rc)= Hj(Fc) otherwise JHJ(FC) O Hj(F c) if F has a boundary otherwise , g.ndT = and, whenever Fc has a boundary, Hj(rc)= {geH 1(r c)|g = o onarc}. Norms of functions belonging to ^J(fi), ^(F) and HS(T C) are denoted by A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL124 A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. AN ANALYSIS OF THE SCHARFETTER-GUMMEL BOX METHOD FOR THE SEMICONDUCTOR DEVICE EQUATIONS 127 where Th dénotes a triangulation of O with each triangle t having diameter less than or equal to h and h0 is a positive constant which is smaller than the diameter of H. For each Th e TS, let Xh = {x,}^ dénote the vertices of Th and Eh = {et}^ the edges of Th.We assume that the nodes in Xh and the edges in Eh are numbered such thatX^ = {*;}^ and E'h = {et}^ GALERKIN TIME-STEPPING METHODS FOR NONLINEAR … GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS 263 in a tube T u,T u:= {v ∈ V:min t u(t)−v≤ 1}, around the solutionu, uniformly in t, with a constant λ¯ less than one. It is easily seen that (1.4) can be written in the form of a G˚arding-typeinequality,
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
SHIGE PENG AND MINGYU XU 336 S. PENG AND M. XU The solution of a BSDE is a couple of progressive measurable processes (Y,Z), which satisfiesY t = ξ + T t g(s,Y s,Z s)ds− T t Z sdB s, (1.1) where B is a Brownian motion. Here ξ is terminal condition and g is a generator. From , we know that when ξ is a square integrable random variable, and g satisfies Lipschitz condition and some integrability ANALYSIS AND FINITE ELEMENT APPROXIMATION OF OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS 715 and For functions defïned on Fc we will use the subspaces Hj(rc) if Fc has a boundary and where Hj(rc)= Hj(Fc) otherwise JHJ(FC) O Hj(F c) if F has a boundary otherwise , g.ndT = and, whenever Fc has a boundary, Hj(rc)= {geH 1(r c)|g = o onarc}. Norms of functions belonging to ^J(fi), ^(F) and HS(T C) are denoted by A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of CONFORMING AND NONCONFORMING FINITE ELEMENT METHODS FOR METHODS FOR SOLVING THE STATIONARY STOKES EQUATIONS 37 In order to approximate problems (2.13) or (2.15), we first construct a triangulation T5fc of the set Q with nondegenerate JV-simplices i£(i.e. triangles if N = 2 or tetrahedrons if N = 3) with diameters <h.
SEMI–SMOOTH NEWTON METHODS FOR VARIATIONAL … 44 K. ITO AND K. KUNISCH Let us consider Newton–differentiability of the max–operator. For this purpose X denotes a function space of real–valued functions on Ω ⊂ Rn and max(0,y) is the pointwise max–operation.For δ ∈ R we introduce candidates for the generalized derivative of the form AN ANALYSIS TECHNIQUE FOR STABILIZED FINITE ELEMENT 58 T. CHACON REBOLLO constructed with the mini-element. It is a direct consequence of the fact that this element satis es the discrete inf-sup condition. Such analysis is FINITE ELEMENT APPROXIMATIONS OF THE THREE DIMENSIONAL 982 S.C. BRENNER AND M. NEILAN Remark 2.1. The norms (2.1)–(2.4) are well-defined for functions in W 3, (T h). Let k be an integer greater than or equal to three and define the finite element space V h ⊂ H1(Ω) as follows: • if T ∈T h does not have a curved face, then v T is a polynomial of (total) degree ≤ k in the rectilinear coordinates for T; • if T ∈T h has one curvedC .G.MAKRIDAKIS P
jom matheuatical uodelung and numerical analysis fflmmh modelisation mathematique et analyse numerique (vol 29, n° 2, 1995, p 171 a 197) time-discrete finite element schemes for maxwell's TIME DISCRETIZATION OF PARABOLIC PROBLEMS BY THE mathematlcalmooeujhganohumericalanalysts mooÉusat1on mathÉmatique et analyse numÉrique (vol. 19, nû 4,1985, p. 611 à 643) time discretization of parabolic TOME 19, N 1 (1985), P. 7-32. mathematica!. modbung and numengal analysts modÉlisation mathÉmatique et analyse numÉrique (vol 19, n° 1, 1985, p 7 à 32) mixed and nonconforming finite element methods : APPROXIMATION BY FINITE ELEMENT FUNCTIONS USING LOCAL APPROXIMATION BY UNITE ELEMENT FONCTIONS 79 The functions 7} is bounded by c. H4. For any D 3), all the angles of the T{s are ^ c > 0. ON A CLASS OF IMPLICIT AND EXPLICIT SCHEMES OF VAN-LEER IMPLICIT AND EXPLICIT SCHEMES OF VAN-LEER TYPE 263 for all 4> C°°(K x K+) with compact support in RxR+, and ^ 0, where y\ is the entropy function and F the entropy flux associated with the A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL124 A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. AN ANALYSIS OF THE SCHARFETTER-GUMMEL BOX METHOD FOR THE SEMICONDUCTOR DEVICE EQUATIONS 127 where Th dénotes a triangulation of O with each triangle t having diameter less than or equal to h and h0 is a positive constant which is smaller than the diameter of H. For each Th e TS, let Xh = {x,}^ dénote the vertices of Th and Eh = {et}^ the edges of Th.We assume that the nodes in Xh and the edges in Eh are numbered such thatX^ = {*;}^ and E'h = {et}^ GALERKIN TIME-STEPPING METHODS FOR NONLINEAR … GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS 263 in a tube T u,T u:= {v ∈ V:min t u(t)−v≤ 1}, around the solutionu, uniformly in t, with a constant λ¯ less than one. It is easily seen that (1.4) can be written in the form of a G˚arding-typeinequality,
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
SHIGE PENG AND MINGYU XU 336 S. PENG AND M. XU The solution of a BSDE is a couple of progressive measurable processes (Y,Z), which satisfiesY t = ξ + T t g(s,Y s,Z s)ds− T t Z sdB s, (1.1) where B is a Brownian motion. Here ξ is terminal condition and g is a generator. From , we know that when ξ is a square integrable random variable, and g satisfies Lipschitz condition and some integrability ANALYSIS AND FINITE ELEMENT APPROXIMATION OF OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS 715 and For functions defïned on Fc we will use the subspaces Hj(rc) if Fc has a boundary and where Hj(rc)= Hj(Fc) otherwise JHJ(FC) O Hj(F c) if F has a boundary otherwise , g.ndT = and, whenever Fc has a boundary, Hj(rc)= {geH 1(r c)|g = o onarc}. Norms of functions belonging to ^J(fi), ^(F) and HS(T C) are denoted by A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract A REMARK ON UZAWA’S ALGORITHM AND AN APPLICATION TO MEAN1 A REMARK ON UZAWA’S ALGORITHM 1057 Then, for any 0 ∈ 2, if < 2 2, (2.4) defines indeed a sequence( ∈N and ( ∈N converges toward *in 1. Proof. First let us remark that for any 0 ∈ 2, the sequence ( ∈N is well de ned. Indeed the second line A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL124 A NUMERICAL ALGORITHM FOR L2 SEMI-DISCRETE OPTIMAL TRANSPORT IN 3D 1695 The pushforwards of the two projections (P1)γ and (P2)γ are called the marginals of γ.The probability measures γ in Π(μ,ν), i.e. that have μ and ν as marginals, are called transport plans.Among the transport plans, those that are in the form (Id×T)μ correspond to a transport map T. AN ANALYSIS OF THE SCHARFETTER-GUMMEL BOX METHOD FOR THE SEMICONDUCTOR DEVICE EQUATIONS 127 where Th dénotes a triangulation of O with each triangle t having diameter less than or equal to h and h0 is a positive constant which is smaller than the diameter of H. For each Th e TS, let Xh = {x,}^ dénote the vertices of Th and Eh = {et}^ the edges of Th.We assume that the nodes in Xh and the edges in Eh are numbered such thatX^ = {*;}^ and E'h = {et}^ GALERKIN TIME-STEPPING METHODS FOR NONLINEAR … GALERKIN TIME-STEPPING METHODS FOR NONLINEAR PARABOLIC EQUATIONS 263 in a tube T u,T u:= {v ∈ V:min t u(t)−v≤ 1}, around the solutionu, uniformly in t, with a constant λ¯ less than one. It is easily seen that (1.4) can be written in the form of a G˚arding-typeinequality,
HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of NEW EFFICIENT BOUNDARY CONDITIONS FOR INCOMPRESSIBLE EFFICIENT BOUNDARY CONDITIONS FOR NAVIER-STOKES EQUATIONS 821 which is the natural condition. Moreover for Navier-Stokes flow, when OLX 1/2, ct2 - a3 and U. n 5= 0 on FNx (0, T) we get again this condition with0(a)= a~ .
SHIGE PENG AND MINGYU XU 336 S. PENG AND M. XU The solution of a BSDE is a couple of progressive measurable processes (Y,Z), which satisfiesY t = ξ + T t g(s,Y s,Z s)ds− T t Z sdB s, (1.1) where B is a Brownian motion. Here ξ is terminal condition and g is a generator. From , we know that when ξ is a square integrable random variable, and g satisfies Lipschitz condition and some integrability ANALYSIS AND FINITE ELEMENT APPROXIMATION OF OPTIMAL CONTROL PROBLEMS FOR THE NAVIER-STOKES EQUATIONS 715 and For functions defïned on Fc we will use the subspaces Hj(rc) if Fc has a boundary and where Hj(rc)= Hj(Fc) otherwise JHJ(FC) O Hj(F c) if F has a boundary otherwise , g.ndT = and, whenever Fc has a boundary, Hj(rc)= {geH 1(r c)|g = o onarc}. Norms of functions belonging to ^J(fi), ^(F) and HS(T C) are denoted by A POSTERIORI ERROR ESTIMATES FOR NONLINEAR PROBLEMS. L R 818 R. VERFÜRTH Here, F e Cl(X,Y*) and F h e C(Xk, F* ), X^ c: X and F^ c F are finite dimensional subspaces of the Banach spaces X and F, and * dénotes the dual of a Banach space» In applications, X will be a suitable subspace of a W ' r-space.In order to obtain Lr-estimates we must enlarge the space X and restrict the space F.To this end we ERROR ESTIMATES FOR MIXED METHODS ERROR ESTIMATES FOR MIXED METHODS 251 There are other problems of a similar nature, however, where attempts at using the ideas of were not entirely successful since not all of the abstract HARTREE-FOCK THEORY IN NUCLEAR PHYSICS HARTREE-FOCK EQUATIONS 573 Section XI is devoted to various considérations on time-dependent Hartree-Fock (TDHF in short) équations such as the orbital stability of the minima of CONFORMING AND NONCONFORMING FINITE ELEMENT METHODS FOR METHODS FOR SOLVING THE STATIONARY STOKES EQUATIONS 37 In order to approximate problems (2.13) or (2.15), we first construct a triangulation T5fc of the set Q with nondegenerate JV-simplices i£(i.e. triangles if N = 2 or tetrahedrons if N = 3) with diameters <h.
SEMI–SMOOTH NEWTON METHODS FOR VARIATIONAL … 44 K. ITO AND K. KUNISCH Let us consider Newton–differentiability of the max–operator. For this purpose X denotes a function space of real–valued functions on Ω ⊂ Rn and max(0,y) is the pointwise max–operation.For δ ∈ R we introduce candidates for the generalized derivative of the form AN ANALYSIS TECHNIQUE FOR STABILIZED FINITE ELEMENT 58 T. CHACON REBOLLO constructed with the mini-element. It is a direct consequence of the fact that this element satis es the discrete inf-sup condition. Such analysis is FINITE ELEMENT APPROXIMATIONS OF THE THREE DIMENSIONAL 982 S.C. BRENNER AND M. NEILAN Remark 2.1. The norms (2.1)–(2.4) are well-defined for functions in W 3, (T h). Let k be an integer greater than or equal to three and define the finite element space V h ⊂ H1(Ω) as follows: • if T ∈T h does not have a curved face, then v T is a polynomial of (total) degree ≤ k in the rectilinear coordinates for T; • if T ∈T h has one curvedC .G.MAKRIDAKIS P
jom matheuatical uodelung and numerical analysis fflmmh modelisation mathematique et analyse numerique (vol 29, n° 2, 1995, p 171 a 197) time-discrete finite element schemes for maxwell's TIME DISCRETIZATION OF PARABOLIC PROBLEMS BY THE mathematlcalmooeujhganohumericalanalysts mooÉusat1on mathÉmatique et analyse numÉrique (vol. 19, nû 4,1985, p. 611 à 643) time discretization of parabolic TOME 19, N 1 (1985), P. 7-32. mathematica!. modbung and numengal analysts modÉlisation mathÉmatique et analyse numÉrique (vol 19, n° 1, 1985, p 7 à 32) mixed and nonconforming finite element methods : APPROXIMATION BY FINITE ELEMENT FUNCTIONS USING LOCAL APPROXIMATION BY UNITE ELEMENT FONCTIONS 79 The functions 7} is bounded by c. H4. For any D 3), all the angles of the T{s are ^ c > 0. ON A CLASS OF IMPLICIT AND EXPLICIT SCHEMES OF VAN-LEER IMPLICIT AND EXPLICIT SCHEMES OF VAN-LEER TYPE 263 for all 4> C°°(K x K+) with compact support in RxR+, and ^ 0, where y\ is the entropy function and F the entropy flux associated with the By using this website, you agree that EDP Sciences may store web audience measurement cookies and, on some pages, cookies from social networks. More information and setup OKMenu
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Vol. 53 (5) (2019)
Vol. 53 (4) (2019)
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ESAIM: MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS (ESAIM: M2AN) _ESAIM: M2AN _ publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis.Read more
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ON EULER PRECONDITIONED SHSS ITERATIVE METHOD FOR A CLASS OF COMPLEX SYMMETRIC LINEAR SYSTEMS Cheng-Liang Li and Chang-Feng Ma ESAIM: M2AN, 53 5 (2019) 1607-1627 Published online: 09 August 2019*
ON A CLASS OF DERIVATIVE NONLINEAR SCHRÖDINGER-TYPE EQUATIONS IN TWOSPATIAL DIMENSIONS
Jack Arbunich, Christian Klein and Christof Sparber ESAIM: M2AN, 53 5 (2019) 1477-1505 Published online: 06 August 2019*
MULTILEVEL QUASI-MONTE CARLO INTEGRATION WITH PRODUCT WEIGHTS FOR ELLIPTIC PDES WITH LOGNORMAL COEFFICIENTS L. Herrmann and C. Schwab ESAIM: M2AN, 53 5 (2019) 1507-1552 Published online: 06 August 2019*
RAVIART–THOMAS FINITE ELEMENTS OF PETROV–GALERKIN TYPE Francois Dubois, Isabelle Greff and Charles Pierre ESAIM: M2AN, 53 5 (2019) 1553-1576 Published online: 06 August 2019*
ANALYSIS OF THE ERROR IN AN ITERATIVE ALGORITHM FOR ASYMPTOTIC REGULATION OF LINEAR DISTRIBUTED PARAMETER CONTROL SYSTEMS Eugenio Aulisa, David S. Gilliam and Thanuka W. Pathiranage ESAIM: M2AN, 53 5 (2019) 1577-1606 Published online: 06 August 2019*
A POSITIVITY-PRESERVING CENTRAL-UPWIND SCHEME FOR ISENTROPIC TWO-PHASE FLOWS THROUGH DEVIATED PIPES Gerardo Hernandez-Duenas, Ulises Velasco-García and Jorge X.Velasco-Hernández
ESAIM: M2AN, 53 5 (2019) 1433-1457 Published online: 23 July 2019*
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CONVERGENCE OF THE FINITE VOLUME METHOD ON A SCHWARZSCHILD BACKGROUND Shijie Dong and Philippe G. LeFloch ESAIM: M2AN, 53 5 (2019) 1459-1476 Published online: 23 July 2019*
A THREE-PHASE FLOW MODEL WITH TWO MISCIBLE PHASES J.-M. Hérard and H. Mathis ESAIM: M2AN, 53 4 (2019) 1373-1389 Published online: 11 July 2019*
A DYNAMIC MULTILAYER SHALLOW WATER MODEL FOR POLYDISPERSESEDIMENTATION
Raimund Bürger, Enrique D. Fernández-Nieto and Víctor Osores ESAIM: M2AN, 53 4 (2019) 1391-1432 Published online: 11 July 2019MOST READ ARTICLES
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THE MATHEMATICAL THEORY OF LOW MACH NUMBER FLOWSSteven Schochet
ESAIM: M2AN, 39 3 (2005) 441-458 Published online: 15 June 200536
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COUPLAGE DES ÉQUATIONS DE NAVIER-STOKES ET DE LA CHALEUR : LE MODÈLE ET SON APPROXIMATION PAR ÉLÉMENTS FINIS Christine Bernardi, Brigitte Métivet and Bernadette Pernaud-Thomas ESAIM: M2AN, 29 7 (1995) 871-921 Published online: 31 January 201725
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QUASI-CONVEXITY, STRICTLY QUASI-CONVEXITY AND PSEUDO-CONVEXITY OF COMPOSITE OBJECTIVE FUNCTIONSBernard Bereanu
R.A.I.R.O., 6 R1 (1972) 15-26 Published online: 01 February 201720
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A HYBRID SCHEME TO COMPUTE CONTACT DISCONTINUITIES IN ONE-DIMENSIONALEULER SYSTEMS
Thierry Gallouët, Jean-Marc Hérard and Nicolas Seguin ESAIM: M2AN, 36 6 (2002) 1133-1159 Published online: 15 January 200313
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CONVERGENCE OF THE FINITE VOLUME METHOD ON A SCHWARZSCHILD BACKGROUND Shijie Dong and Philippe G. LeFloch ESAIM: M2AN, 53 5 (2019) 1459-1476 Published online: 23 July 2019313
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THE MATHEMATICAL THEORY OF LOW MACH NUMBER FLOWSSteven Schochet
ESAIM: M2AN, 39 3 (2005) 441-458 Published online: 15 June 2005233
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COUPLAGE DES ÉQUATIONS DE NAVIER-STOKES ET DE LA CHALEUR : LE MODÈLE ET SON APPROXIMATION PAR ÉLÉMENTS FINIS Christine Bernardi, Brigitte Métivet and Bernadette Pernaud-Thomas ESAIM: M2AN, 29 7 (1995) 871-921 Published online: 31 January 201784
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QUASI-CONVEXITY, STRICTLY QUASI-CONVEXITY AND PSEUDO-CONVEXITY OF COMPOSITE OBJECTIVE FUNCTIONSBernard Bereanu
R.A.I.R.O., 6 R1 (1972) 15-26 Published online: 01 February 201774
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THE CORRECT USE OF THE LAX–FRIEDRICHS METHODMichael Breuß
ESAIM: M2AN, 38 3 (2004) 519-540 Published online: 15 June 200458
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HOMOGENIZATION OF A MONOTONE PROBLEM IN A DOMAIN WITH OSCILLATINGBOUNDARY
Dominique Blanchard, Luciano Carbone and Antonio Gaudiello ESAIM: M2AN, 33 5 (1999) 1057-1070 Published online: 15 August 2002776
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COUPLAGE DES ÉQUATIONS DE NAVIER-STOKES ET DE LA CHALEUR : LE MODÈLE ET SON APPROXIMATION PAR ÉLÉMENTS FINIS Christine Bernardi, Brigitte Métivet and Bernadette Pernaud-Thomas ESAIM: M2AN, 29 7 (1995) 871-921 Published online: 31 January 2017704
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THE MATHEMATICAL THEORY OF LOW MACH NUMBER FLOWSSteven Schochet
ESAIM: M2AN, 39 3 (2005) 441-458 Published online: 15 June 2005331
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THE CORRECT USE OF THE LAX–FRIEDRICHS METHODMichael Breuß
ESAIM: M2AN, 38 3 (2004) 519-540 Published online: 15 June 2004249
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QUASI-CONVEXITY, STRICTLY QUASI-CONVEXITY AND PSEUDO-CONVEXITY OF COMPOSITE OBJECTIVE FUNCTIONSBernard Bereanu
R.A.I.R.O., 6 R1 (1972) 15-26 Published online: 01 February 2017201
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HOMOGENIZATION OF A MONOTONE PROBLEM IN A DOMAIN WITH OSCILLATINGBOUNDARY
Dominique Blanchard, Luciano Carbone and Antonio Gaudiello ESAIM: M2AN, 33 5 (1999) 1057-1070 Published online: 15 August 2002* Submit your paper
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