Journal
NUMERISCHE MATHEMATIK
Volume 145, Issue 3, Pages 473-511Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00211-020-01121-3
Keywords
Primary 74S10; 65M12; 92C15; Secondary 45K05; 92D25; 47N60
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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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