A linear scheme to approximate nonlinear cross-diffusion systems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 6, pp. 1141-1161.

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.

DOI : 10.1051/m2an/2011010
Classification : 35K55, 35K57, 65M12, 92D25
Mots clés : cross-diffusion systems, nonlinear diffusion, discrete-time schemes, numerical schemes, reaction-diffusion system approximations
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     title = {A linear scheme to approximate nonlinear cross-diffusion systems},
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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://www.numdam.org/articles/10.1051/m2an/2011010/

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