A nonlinear time compactness result and ...
Type de document :
Compte-rendu et recension critique d'ouvrage
Titre :
A nonlinear time compactness result and applications to discretization of degenerate parabolic-elliptic PDEs
Auteur(s) :
Andreianov, Boris [Auteur]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Cancès, Clément [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Ndoye, Moussa [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Cancès, Clément [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Ndoye, Moussa [Auteur]
Laboratoire Jacques-Louis Lions [LJLL]
Titre de la revue :
Journal of Functional Analysis
Pagination :
3633-3670
Éditeur :
Elsevier
Date de publication :
2017
ISSN :
0022-1236
Mot(s)-clé(s) en anglais :
degenerate parabolic equations
strong compactness
gradient scheme
weakly convergent sequences
strong compactness
gradient scheme
weakly convergent sequences
Discipline(s) HAL :
Mathématiques [math]/Analyse fonctionnelle [math.FA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]
Résumé en anglais : [en]
We propose a discrete functional analysis result suitable for proving compactness in the framework of fully discrete approximations of strongly degenerate parabolic problems. It is based on the original exploitation of a ...
Lire la suite >We propose a discrete functional analysis result suitable for proving compactness in the framework of fully discrete approximations of strongly degenerate parabolic problems. It is based on the original exploitation of a result related to compensated compactness rather than on a classical estimate on the space and time translates in the spirit of Simon (Ann. Mat. Pura Appl. 1987). Our approach allows to handle various numerical discretizations both in the space variables and in the time variable. In particular, we can cope quite easily with variable time steps and with multistep time differentiation methods like, e.g., the backward differentiation formula of order 2 (BDF2) scheme. We illustrate our approach by proving the convergence of a two-point flux Finite Volume in space and BDF2 in time approximation of the porous medium equation.Lire moins >
Lire la suite >We propose a discrete functional analysis result suitable for proving compactness in the framework of fully discrete approximations of strongly degenerate parabolic problems. It is based on the original exploitation of a result related to compensated compactness rather than on a classical estimate on the space and time translates in the spirit of Simon (Ann. Mat. Pura Appl. 1987). Our approach allows to handle various numerical discretizations both in the space variables and in the time variable. In particular, we can cope quite easily with variable time steps and with multistep time differentiation methods like, e.g., the backward differentiation formula of order 2 (BDF2) scheme. We illustrate our approach by proving the convergence of a two-point flux Finite Volume in space and BDF2 in time approximation of the porous medium equation.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Projet ANR :
Collections :
Source :
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