%0 Journal Article
%T Numerical resolution of an anisotropic non-linear diffusion problem
%A St¨¦phane Brull
%A Fabrice Deluzet
%A Alexandre Mouton
%J Mathematics
%D 2012
%I arXiv
%X This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter \varepsilon, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable vector function b. The equation being supplemented with Neumann boundary conditions, the limit \varepsilon \infty 0 is demonstrated to be a singular perturbation of the original diffusion equation. To address efficiently this problem, an Asymptotic-Preserving scheme is derived. This numerical method does not require the use of coordinates adapted to the anisotropy direction and exhibits an accuracy as well as a computational cost independent of the anisotropy strength.
%U http://arxiv.org/abs/1210.0681v1