CONVERGENCE OF A FINITE VOLUME SCHEME FOR A SYSTEM OF INTERACTING SPECIES WITH CROSS-DIFFUSION

Abstract : In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to establish positivity in order to obtain a discrete energy estimate to obtain compactness. We numerically observe the convergence to reference solutions with a first order accuracy in space. Moreover we recover segregated stationary states in spite of the regularising effect of the self-diffusion. However, if the self-diffusion or the cross-diffusion is strong enough, mixing occurs while both densities remain continuous.
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Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01764444
Contributeur : Francis Filbet <>
Soumis le : jeudi 12 avril 2018 - 00:33:26
Dernière modification le : vendredi 14 septembre 2018 - 09:16:06

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  • HAL Id : hal-01764444, version 1

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José Carrillo, Francis Filbet, Markus Schmidtchen. CONVERGENCE OF A FINITE VOLUME SCHEME FOR A SYSTEM OF INTERACTING SPECIES WITH CROSS-DIFFUSION. 2018. 〈hal-01764444〉

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