Numerical resolution of a highly anisotropic two-dimensional elliptic problem by a parameterization method

Numerical resolution of a highly anisotropic two-dimensional elliptic problem by a parameterization method. We introduce a numerical method for solving an anisotropic elliptic problem. We address the case where the direction of the anisotropy varies, and the anisotropy is high. A finite volume scheme is implemented to solve the problem for small anisotropy ratio, then the parameterization method consists in devising an extrapolation of the solution of the anisotropic problem by combining solutions of a sequence of isotropic problems. (C) 2003 Academie des sciences. Publie par Editions scientifiques et medicales Elsevier SAS. Tous droits reserves.