Titre :

Large-time behaviour of a family of finite volume schemes for boundary-driven convection-diffusion equations

Auteur(s) :

Chainais-Hillairet, Claire [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Herda, Maxime [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]

Titre de la revue :

IMA Journal of Numerical Analysis

Pagination :

2473-2505

Éditeur :

Oxford University Press (OUP)

Date de publication :

2020-10-01

ISSN :

0272-4979

Mot(s)-clé(s) en anglais :

Long-time behavior
Finite volume methods
Mixed boundary conditions
Entropy methods

Discipline(s) HAL :

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

Résumé en anglais : [en]

We are interested in the large-time behaviour of solutions to finite volume discretizations of convection–diffusion equations or systems endowed with nonhomogeneous Dirichlet- and Neumann-type boundary conditions. Our ...
Lire la suite >We are interested in the large-time behaviour of solutions to finite volume discretizations of convection–diffusion equations or systems endowed with nonhomogeneous Dirichlet- and Neumann-type boundary conditions. Our results concern various linear and nonlinear models such as Fokker–Planck equations, porous media equations or drift–diffusion systems for semiconductors. For all of these models, some relative entropy principle is satisfied and implies exponential decay to the stationary state. In this paper we show that in the framework of finite volume schemes on orthogonal meshes, a large class of two-point monotone fluxes preserves this exponential decay of the discrete solution to the discrete steady state of the scheme. This includes for instance upwind and centred convections or Scharfetter–Gummel discretizations. We illustrate our theoretical results on several numerical test cases.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
MOdèles, Oscillations et SchEmas NUmeriques
Fondation Sciences Mathématiques de Paris

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL