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Article Dans Une Revue Communications in Mathematical Sciences Année : 2015

Numerical resolution of an anisotropic non-linear diffusion problem

Résumé

This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter ε, 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 ε → 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.
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Dates et versions

hal-00735863 , version 1 (28-09-2012)
hal-00735863 , version 2 (28-09-2012)

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Stéphane Brull, Fabrice Deluzet, Alexandre Mouton. Numerical resolution of an anisotropic non-linear diffusion problem. Communications in Mathematical Sciences, 2015, vol. 13 (1), p. 203 - 224. ⟨10.4310/CMS.2015.v13.n1.a10⟩. ⟨hal-00735863v2⟩
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