Title :

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

Author(s) :

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

Journal title :

IMA Journal of Numerical Analysis

Pages :

2473-2505

Publisher :

Oxford University Press (OUP)

Publication date :

2020-10-01

ISSN :

0272-4979

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

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