Duality-based asymptotic-preserving method for highly Anisotropic diffusion equations

Abstract

The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic preserving reformulation of the original system, permitting an accurate resolution independently of the anisotropy strength and without the need of a mesh adapted to this anisotropy. The counterpart of this original procedure is the larger system size, enlarged by adding auxiliary variables and Lagrange multipliers. This Asymptotic-Preserving method generalizes the method investigated in a previous paper [P. Degond, F. Deluzet, and C. Negulescu, Multiscale Model. Simul., 8(2), 645-666, 2009/10] to the case of an arbitrary anisotropy direction field. © 2012 International Press.