TY - JOUR
T1 - A linear scheme to approximate nonlinear cross-diffusion systems
AU - Murakawa, Hideki
N1 - Funding Information:
This work was supported by Grant-in-Aid for Young Scientists (B)(No. 22740058) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
PY - 2011/11
Y1 - 2011/11
N2 - 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.
AB - 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.
KW - Cross-diffusion systems
KW - Discrete-time schemes
KW - Nonlinear diffusion
KW - Numerical schemes
KW - Reaction-diffusion system approximations
UR - https://www.scopus.com/pages/publications/80051997620
UR - https://www.scopus.com/pages/publications/80051997620#tab=citedBy
U2 - 10.1051/m2an/2011010
DO - 10.1051/m2an/2011010
M3 - Article
AN - SCOPUS:80051997620
SN - 2822-7840
VL - 45
SP - 1141
EP - 1161
JO - ESAIM: Mathematical Modelling and Numerical Analysis
JF - ESAIM: Mathematical Modelling and Numerical Analysis
IS - 6
ER -