Volume 57, Number 3, May-June 2023
|Page(s)||1589 - 1617|
|Published online||26 May 2023|
Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system
Inria, Univ. Lille, CNRS, UMR 8524–Laboratoire Paul Painlevé, 59000 Lille, France
2 Université de Technologie de Compiègne, LMAC, 60200 Compigne, France
* Corresponding author: email@example.com
Accepted: 31 March 2023
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.
Mathematics Subject Classification: 65M08 / 65M12 / 35K51 / 35Q92 / 92D25
Key words: Nonlocal cross-diffusion / finite volume schemes / entropy method / convergence
© The authors. Published by EDP Sciences, SMAI 2023
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