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arXiv · 1804.04385

Convergence of a Finite Volume Scheme for a System of Interacting Species with Cross-Diffusion

José A. Carrillo·Francis Filbet·Markus Schmidtchen
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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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José A. Carrillo, Francis Filbet, Markus Schmidtchen. 2018-04-12. Convergence of a Finite Volume Scheme for a System of Interacting Species with Cross-Diffusion. https://arxiv.org/abs/1804.04385

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