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

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2018
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01894884
Contributeur : Flore Nabet <>
Soumis le : vendredi 12 octobre 2018 - 23:15:10
Dernière modification le : mercredi 23 janvier 2019 - 10:29:27
Document(s) archivé(s) le : dimanche 13 janvier 2019 - 16:21:11

Fichier

CNV.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01894884, version 1

Citation

Clément Cancès, Flore Nabet, Martin Vohralík. Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations. 2018. 〈hal-01894884〉

Partager

Métriques

Consultations de la notice

85

Téléchargements de fichiers

103