An asymptotic-preserving method for highly anisotropic elliptic equations based on a MicroMacro decomposition
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<??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/?. 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) 131] and its considerable advantages are pointed out.
asymptotic preserving scheme anisotropic diffusion finite element method