NUMERICAL RESOLUTION OF AN ANISOTROPIC ...
Document type :
Compte-rendu et recension critique d'ouvrage
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]
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
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 >
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
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