Details

Autor(en) / Beteiligte

• Carrillo, José A.
• Filbet, Francis
• Schmidtchen, Markus

Titel

Convergence of a finite volume scheme for a system of interacting species with cross-diffusion

Ist Teil von

• Numerische Mathematik, 2020-07, Vol.145 (3), p.473-511

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2020

Quelle

SpringerNature Journals

Beschreibungen/Notizen

• 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.