Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911759902703616 |
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| author | Herda, Maxime Zurek, Antoine |
| author_facet | Herda, Maxime Zurek, Antoine |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_01928 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system Herda, Maxime Zurek, Antoine Numerical Analysis 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. |
| title | Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2207.01928 |