An asymptotic-preserving method for highly anisotropic elliptic equations based on a Micro-Macro decomposition

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Degond, Pierre^1,2  Lozinski, Alexei¹  Narski, Jacek¹ 

[1] Univ Toulouse, UPS, INSA, UTM,Inst Math Toulouse,UT1, F-31062 Toulouse, France

[2] CNRS, Inst Math Toulouse, UMR 5219, F-31062 Toulouse, France

关键词: Anisotropic diffusion;    Asymptotic preserving scheme;    Finite element method;   

DOI  :  10.1016/j.jcp.2011.11.040

来源: Elsevier

【 摘 要 】

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 < epsilon << 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/epsilon. The mathematical approach and the numerical scheme are different from those presented in the previous work [P. Degond, F. Deluzet, A. Lozinski, J. Narski, C. Negulescu, Duality-based asymptotic-preserving method for highly anisotropic diffusion equations, Communications in Mathematical Sciences 10 (1) (2012) 1-31] and its considerable advantages are pointed out. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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