Convergence and a posteriori error analysis ...
Type de document :
Compte-rendu et recension critique d'ouvrage
DOI :
Titre :
Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations
Auteur(s) :
Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Nabet, Flore [Auteur correspondant]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Vohralík, Martin [Auteur]
Simulation for the Environment: Reliable and Efficient Numerical Algorithms [SERENA]
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Reliable numerical approximations of dissipative systems [RAPSODI]
Nabet, Flore [Auteur correspondant]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Vohralík, Martin [Auteur]
Simulation for the Environment: Reliable and Efficient Numerical Algorithms [SERENA]
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Titre de la revue :
Mathematics of Computation
Pagination :
517-563
Éditeur :
American Mathematical Society
Date de publication :
2021
ISSN :
0025-5718
Mot(s)-clé(s) en anglais :
Convergence
Degenerate parabolic equation
Equilibrated flux
Energy-stable discretization
Local conservation
Fokker-Planck equation
A posteriori error estimate
Degenerate parabolic equation
Equilibrated flux
Energy-stable discretization
Local conservation
Fokker-Planck equation
A posteriori error estimate
Discipline(s) HAL :
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Résumé en anglais : [en]
We propose a finite element scheme for numerical approximation of degenerate parabolic problems in the form of a nonlinear anisotropic Fokker-Planck equation. The scheme is energy-stable, only involves physically motivated ...
Lire la suite >We propose a finite element scheme for numerical approximation of degenerate parabolic problems in the form of a nonlinear anisotropic Fokker-Planck equation. The scheme is energy-stable, only involves physically motivated quantities in its definition, and is able to handle general unstructured grids. Its convergence is rigorously proven thanks to compactness arguments, under very general assumptions. Although the scheme is based on Lagrange finite elements of degree 1, it is locally conservative after a local postprocess giving rise to an equilibrated flux. This also allows to derive a guaranteed a posteriori error estimate for the approximate solution. Numerical experiments are presented in order to give evidence of a very good behavior of the proposed scheme in various situations involving strong anisotropy and drift terms.Lire moins >
Lire la suite >We propose a finite element scheme for numerical approximation of degenerate parabolic problems in the form of a nonlinear anisotropic Fokker-Planck equation. The scheme is energy-stable, only involves physically motivated quantities in its definition, and is able to handle general unstructured grids. Its convergence is rigorously proven thanks to compactness arguments, under very general assumptions. Although the scheme is based on Lagrange finite elements of degree 1, it is locally conservative after a local postprocess giving rise to an equilibrated flux. This also allows to derive a guaranteed a posteriori error estimate for the approximate solution. Numerical experiments are presented in order to give evidence of a very good behavior of the proposed scheme in various situations involving strong anisotropy and drift terms.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Projet ANR :
Collections :
Source :
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