Volume 45, Number 6, November-December 2011
|Page(s)||1141 - 1161|
|Published online||04 July 2011|
A linear scheme to approximate nonlinear cross-diffusion systems*
Faculty of Mathematics, Kyushu University, 744 Motooka, Nishiku, Fukuoka, 819-0395 Japan. email@example.com
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.
Mathematics Subject Classification: 35K55 / 35K57 / 65M12 / 92D25
Key words: Cross-diffusion systems / nonlinear diffusion / discrete-time schemes / numerical schemes / Reaction-diffusion system approximations
© EDP Sciences, SMAI, 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.