Numerical resolution of an anisotropic non-linear diffusion problem
Numerical Analysis
2012-10-03 v1
Abstract
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.
Cite
@article{arxiv.1210.0681,
title = {Numerical resolution of an anisotropic non-linear diffusion problem},
author = {Stéphane Brull and Fabrice Deluzet and Alexandre Mouton},
journal= {arXiv preprint arXiv:1210.0681},
year = {2012}
}