Titre :

Large time behavior of nonlinear finite volume schemes for convection-diffusion equations

Auteur(s) :

Cancès, Clément [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Chainais-Hillairet, Claire [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Herda, Maxime [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Krell, Stella [Auteur]
COmplex Flows For Energy and Environment [COFFEE]
Laboratoire Jean Alexandre Dieudonné [LJAD]

Titre de la revue :

SIAM Journal on Numerical Analysis

Pagination :

2544-2571

Éditeur :

Society for Industrial and Applied Mathematics

Date de publication :

2020-09-16

ISSN :

0036-1429

Mot(s)-clé(s) en anglais :

Finite volume methods
Long-time behavior
Entropy methods
Discrete functional inequalities
Logarithmic Sobolev inequalities

Discipline(s) HAL :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

Résumé en anglais : [en]

In this contribution we analyze the large time behavior of a family of nonlinear finite volume schemes for anisotropic convection-diffusion equations set in a bounded bidimensional domain and endowed with either Dirichlet ...
Lire la suite >In this contribution we analyze the large time behavior of a family of nonlinear finite volume schemes for anisotropic convection-diffusion equations set in a bounded bidimensional domain and endowed with either Dirichlet and / or no-flux boundary conditions. We show that solutions to the two-point flux approximation (TPFA) and discrete duality finite volume (DDFV) schemes under consideration converge exponentially fast toward their steady state. The analysis relies on discrete entropy estimates and discrete functional inequalities. As a biproduct of our analysis, we establish new discrete Poincaré-Wirtinger, Beckner and logarithmic Sobolev inequalities. Our theoretical results are illustrated by numerical simulations.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Modèles multi-échelles et simulation numérique hybride de semi-conducteurs

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL