Convergence and a posteriori error analysis ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations
Author(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]
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Simulation for the Environment: Reliable and Efficient Numerical Algorithms [SERENA]
Reliable numerical approximations of dissipative systems [RAPSODI]
Nabet, Flore [Auteur correspondant]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Vohralík, Martin [Auteur]
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Simulation for the Environment: Reliable and Efficient Numerical Algorithms [SERENA]
Journal title :
Mathematics of Computation
Pages :
517-563
Publisher :
American Mathematical Society
Publication date :
2021
ISSN :
0025-5718
English keyword(s) :
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
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
English abstract : [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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
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