Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system

Herda, Maxime; Zurek, Antoine

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1051/m2an/2023032

Title :

Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system

Author(s) :

Herda, Maxime [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Zurek, Antoine [Auteur]
Laboratoire de Mathématiques Appliquées de Compiègne [LMAC]

Journal title :

ESAIM: Mathematical Modelling and Numerical Analysis

Pages :

1589 - 1617

Publisher :

EDP Sciences

Publication date :

2023-05

ISSN :

0764-583X

English keyword(s) :

Nonlocal cross-diffusion
finite volume schemes
entropy method
convergence

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the scheme, derive qualitative properties of ...
Show more >In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the scheme, derive qualitative properties of the solutions and prove its convergence. The proofs rely on a discrete entropy-dissipation inequality, discrete compactness arguments, and on the novel adaptation of the so-called duality method at the discrete level. Finally, thanks to numerical experiments, we investigate the influence of the nonlocality in the system: on convergence properties of the scheme, as an approximation of the local system and on the development of diffusive instabilities.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :