Titre :

On the square-root approximation finite volume scheme for nonlinear drift-diffusion equations

Auteur(s) :

Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Venel, Juliette [Auteur]
Laboratoire de Matériaux Céramiques et de Mathématiques [CERAMATHS]
Université Polytechnique Hauts-de-France [UPHF]

Titre de la revue :

Comptes Rendus. Mathématique

Pagination :

535--558

Éditeur :

Académie des sciences (Paris)

Date de publication :

2023

ISSN :

1631-073X

Mot(s)-clé(s) en anglais :

Nonlinear convection diffusion
finite volume method
energy dissipation
convergence

Discipline(s) HAL :

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

Résumé en anglais : [en]

We study a finite volume scheme for the approximation of the solution to convection diffusion equations with nonlinear convection and Robin boundary conditions. The scheme builds on the interpretation of such a continuous ...
Lire la suite >We study a finite volume scheme for the approximation of the solution to convection diffusion equations with nonlinear convection and Robin boundary conditions. The scheme builds on the interpretation of such a continuous equation as the hydrodynamic limit of some simple exclusion jump process. We show that the scheme admits a unique discrete solution, that the natural bounds on the solution are preserved, and that it encodes the second principle of thermodynamics in the sense that some free energy is dissipated along time. The convergence of the scheme is then rigorously established thanks to compactness arguments. Numerical simulations are finally provided, highlighting the overall good behavior of the scheme.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Systèmes de diffusion croisée sur des domaines en mouvement
Description microscopique des interfaces mobiles

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL