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A linear finite volume method for nonlinear cross-diffusion systems

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Abstract

In this paper, we propose and analyze a linear finite volume scheme for general nonlinear cross-diffusion systems. The scheme consists of discretization of linear elliptic equations and pointwise explicit algebraic corrections at each time step. Therefore, the scheme can be implemented very easily, moreover, it is unconditionally stable. We establish error estimates in the \(L^2\) norm.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, 744 Motooka, Nishiku, Fukuoka, 819-0395, Japan

    Hideki Murakawa

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  1. Hideki Murakawa
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Correspondence to Hideki Murakawa.

Additional information

This work was partially supported by JSPS KAKENHI Grant Numbers 26287025, 26400205 and 15H03635 and JST CREST, Research Area: Modeling Methods allied with Modern Mathematics (Research Supervisor: Takashi Tsuboi ), Project: Theory on mathematical modeling for spatio-temporal patterns arising in biology (Research Director: Shin-Ichiro Ei).

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Murakawa, H. A linear finite volume method for nonlinear cross-diffusion systems. Numer. Math. 136, 1–26 (2017). https://doi.org/10.1007/s00211-016-0832-z

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  • DOI: https://doi.org/10.1007/s00211-016-0832-z

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