Title :

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

Author(s) :

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

Journal title :

Comptes Rendus. Mathématique

Pages :

535--558

Publisher :

Académie des sciences (Paris)

Publication date :

2023

ISSN :

1631-073X

English keyword(s) :

Nonlinear convection diffusion
finite volume method
energy dissipation
convergence

HAL domain(s) :

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

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

Language :

Anglais

Popular science :

Non

ANR Project :

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

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL