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arXiv · 2207.01928

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

Maxime Herda·Antoine Zurek
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Abstract

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.

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Maxime Herda, Antoine Zurek. 2022-07-05. Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system. https://doi.org/10.1051/m2an/2023032

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