Study of an entropy dissipating finite ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
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]
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
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 >
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
Collections :
Source :
Files
- document
- Open access
- Access the document
- main.pdf
- Open access
- Access the document
- 2207.01928
- Open access
- Access the document