BRULL, Stéphane; DELUZET, Fabrice; MOUTON, Alexandre

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BRULL, Stéphane
Institut de Mathématiques de Bordeaux [IMB]

DELUZET, Fabrice
Institut de Mathématiques de Toulouse UMR5219 [IMT]

MOUTON, Alexandre
Laboratoire Paul Painlevé - UMR 8524 [LPP]

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Communications in Mathematical Sciences. 2015

International Press

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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.< Leer menos

Palabras clave en inglés

Anisotropic diffusion problems

Singular perturbation

Asymptotic-Preserving schemes AMS Subject Classification: 35J60

35J62

65M06

65M12

65N06

65N12

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NUMERICAL RESOLUTION OF AN ANISOTROPIC NON-LINEAR DIFFUSION PROBLEM *

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