Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations

Cancès, Clément; Nabet, Flore; Vohralík, Martin

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]

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

Discipline(s) HAL :

Mathématiques [math]/Analyse numérique [math.NA]
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 >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Approche géométrique pour les écoulements en milieux poreux: théorie et numérique
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :