Displaying similar documents to “A linear scheme to approximate nonlinear cross-diffusion systems*”

A linear scheme to approximate nonlinear cross-diffusion systems

Hideki Murakawa (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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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 [ (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...

An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems

Molati, Motlatsi, Murakawa, Hideki

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This paper deals with nonlinear diffusion problems which include the Stefan problem, the porous medium equation and cross-diffusion systems. We provide a linear scheme for these nonlinear diffusion problems. The proposed numerical scheme has many advantages. Namely, the implementation is very easy and the ensuing linear algebraic systems are symmetric, which show low computational cost. Moreover, this scheme has the accuracy comparable to that of the wellstudied nonlinear schemes and...

An asymptotic preserving scheme for model using classical diffusion schemes on unstructured polygonal meshes

Emmanuel Franck, Philippe Hoch, Pierre Navaro, Gérald Samba (2011)

ESAIM: Proceedings

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A new scheme for discretizing the model on unstructured polygonal meshes is proposed. This scheme is designed such that its limit in the diffusion regime is the MPFA-O scheme which is proved to be a consistent variant of the Breil-Maire diffusion scheme. Numerical tests compare this scheme with a derived GLACE scheme for the system.

Max Duarte, Marc Massot, Stéphane Descombes, Christian Tenaud, Thierry Dumont, Violaine Louvet, Frédérique Laurent (2011)

ESAIM: Proceedings

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We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive fronts, spatially very localized. A new resolution strategy was recently introduced ...