Contributions to Books:
A. Jüngel, A. Zurek:
"A converegent structure-preserving finite-volume scheme for the Shigesada-Kawasaki-Teramota population system";
in: "ASC Report 34/2020",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
An implicit Euler ﬁnite-volume scheme for an n-species population cross-diﬀusion system of Shigesada-Kawasaki-Teramoto-type in a bounded domain with no-ﬂux boundary conditions is proposed and analyzed. The scheme preserves the formal gradient-ﬂow or entropy structure and preserves the nonnegativity of the population densities. The
key idea is to consider a suitable mean of the mobilities in such a way that a discrete chain rule is fulﬁlled and a discrete analog of the entropy inequality holds. The existence of ﬁnite-volume solutions, the convergence of the scheme, and the large-time asymptotics
to the constant steady state are proven. Furthermore, numerical experiments in one and two space dimensiona for two and three species are presented. The results are valid for a more general class of cross-diﬀusion systems satisfying some structural conditions.
Cross-diﬀusion system, population dynamics, ﬁnite-volume method, discreteentropy dissipation, convergence of the scheme, large-time asymptotics.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.