NUMERICAL RESOLUTION OF AN ANISOTROPIC NON-LINEAR DIFFUSION PROBLEM *
Language
en
Article de revue
This item was published in
Communications in Mathematical Sciences. 2015
International Press
English Abstract
This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter ǫ, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a ...Read more >
This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter ǫ, 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 ǫ → 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.Read less <
English Keywords
Anisotropic diffusion problems
Singular perturbation
Asymptotic-Preserving schemes AMS Subject Classification: 35J60
35J62
65M06
65M12
65N06
65N12
Origin
Hal imported