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

作者：Degond Pierre; Lozinski Alexei; Narski Jacek^*; Negulescu Claudia

来源：Journal of Computational Physics, 2012, 231(7): 2724-2740.

DOI：10.1016/j.jcp.2011.11.040

• Anisotropic diffusion
• Asymptotic preserving scheme
• Finite element method

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.

• 出版日期2012-4-1