The gradient discretisation method / Jérôme Droniou, Robert Eymard, Thierry Gallouët, ... [et al.]

Auteur: Droniou, Jérôme (1975-) - AuteurCo-auteur: Eymard, Robert (1957-) - Auteur ; Gallouët, Thierry (1953-) - Auteur ; Guichard, Cindy - Auteur ; Herbin, Raphaèle - AuteurType de document: MonographieCollection: Mathématiques et applications ; 82Langue: anglaisPays: SwisseÉditeur: Cham : Springer, 2002Description: 1 vol. (XXIV-497 p.) : ill. en noir et en coul. ; 24 cm ISBN: 9783319790411 ; br. ISSN: 1154-483XRésumé: Publisher’s description: This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray-Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.Bibliographie: Bibliogr. p. 487-493. Index. Sujets MSC: 65-02 Numerical analysis -- Research exposition (monographs, survey articles)
65M12 Numerical analysis -- Partial differential equations, initial value and time-dependent initial-boundary value problems -- Stability and convergence of numerical methods
65M15 Numerical analysis -- Partial differential equations, initial value and time-dependent initial-boundary value problems -- Error bounds
65M60 Numerical analysis -- Partial differential equations, initial value and time-dependent initial-boundary value problems -- Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
En-ligne: Zentralblatt | Springer
Location Call Number Status Date Due
Couloir 12532-01 / Séries SMA (Browse Shelf) Available

Bibliogr. p. 487-493. Index

Publisher’s description: This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray-Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes

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