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arXiv · 1102.0904

An Asymptotic-Preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition

Pierre Degond·Alexei Lozinski·Jacek Narski·Claudia Negulescu
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Abstract

The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter $0<\eps <<1$, the applicability (on cartesian grids) to cases of non-uniform and non-aligned anisotropy fields $b$ and the simple extension to the case of a non-constant anisotropy intensity $1/\eps$. The mathematical approach and the numerical scheme are different from those presented in the previous work [Degond et al. (2010), arXiv:1008.3405v1] and its considerable advantages are pointed out.

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Pierre Degond, Alexei Lozinski, Jacek Narski, Claudia Negulescu. 2011-02-04. An Asymptotic-Preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition. https://doi.org/10.1016/j.jcp.2011.11.040

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