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.
Mots-clés : cross-diffusion systems, nonlinear diffusion, discrete-time schemes, numerical schemes, reaction-diffusion system approximations
@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 },
pages = {1141--1161},
publisher = {EDP-Sciences},
volume = {45},
number = {6},
year = {2011},
doi = {10.1051/m2an/2011010},
mrnumber = {2833176},
zbl = {1269.65090},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2011010/}
}
TY - JOUR AU - Murakawa, Hideki TI - A linear scheme to approximate nonlinear cross-diffusion systems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 1141 EP - 1161 VL - 45 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2011010/ DO - 10.1051/m2an/2011010 LA - en ID - M2AN_2011__45_6_1141_0 ER -
%0 Journal Article %A Murakawa, Hideki %T A linear scheme to approximate nonlinear cross-diffusion systems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 1141-1161 %V 45 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2011010/ %R 10.1051/m2an/2011010 %G en %F M2AN_2011__45_6_1141_0
Murakawa, Hideki. A linear scheme to approximate nonlinear cross-diffusion systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 6, pp. 1141-1161. doi : 10.1051/m2an/2011010. http://archive.numdam.org/articles/10.1051/m2an/2011010/
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