This paper proposes a linear discrete-time scheme for general nonlinear cross-diffusion systems. The scheme can be regarded as an extension of a linear scheme based on the nonlinear Chernoff formula for the degenerate parabolic equations, which proposed by Berger et al. [RAIRO Anal. Numer. 13 (1979) 297-312]. We analyze stability and convergence of the linear scheme. To this end, we apply the theory of reaction-diffusion system approximation. After discretizing the scheme in space, we obtain a versatile, easy to implement and efficient numerical scheme for the cross-diffusion systems. Numerical experiments are carried out to demonstrate the effectiveness of the proposed scheme.
@article{M2AN_2011__45_6_1141_0,
author = {Murakawa, Hideki},
title = {A linear scheme to approximate nonlinear cross-diffusion systems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {45},
year = {2011},
pages = {1141-1161},
doi = {10.1051/m2an/2011010},
mrnumber = {2833176},
zbl = {1269.65090},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2011__45_6_1141_0}
}
Murakawa, Hideki. A linear scheme to approximate nonlinear cross-diffusion systems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 45 (2011) pp. 1141-1161. doi : 10.1051/m2an/2011010. http://gdmltest.u-ga.fr/item/M2AN_2011__45_6_1141_0/
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