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

Herda, Maxime; Zurek, Antoine

Type de document :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1051/m2an/2023032

Titre :

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

Auteur(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]

Titre de la revue :

ESAIM: Mathematical Modelling and Numerical Analysis

Pagination :

1589 - 1617

Éditeur :

EDP Sciences

Date de publication :

2023-05

ISSN :

0764-583X

Mot(s)-clé(s) en anglais :

Nonlocal cross-diffusion
finite volume schemes
entropy method
convergence

Discipline(s) HAL :

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

Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :