Title :

NUMERICAL RESOLUTION OF AN ANISOTROPIC NON-LINEAR DIFFUSION PROBLEM *

Author(s) :

Brull, Stéphane [Auteur]
Institut de Mathématiques de Bordeaux [IMB]
Deluzet, Fabrice [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Mouton, Alexandre [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Communications in Mathematical Sciences

Publisher :

International Press

Publication date :

2015

ISSN :

1539-6746

English keyword(s) :

Anisotropic diffusion problems
Singular perturbation
Asymptotic-Preserving schemes AMS Subject Classification: 35J60
35J62
65M06
65M12
65N06
65N12

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

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 ...
Show 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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL