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arXiv · 1008.3405

Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations

Pierre Degond·Fabrice Deluzet·Alexei Lozinski·Jacek Narski·Claudia Negulescu
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Abstract

The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic preserving reformulation of the original system, permitting an accurate resolution independently of the anisotropy strength and without the need of a mesh adapted to this anisotropy. The counterpart of this original procedure is the larger system size, enlarged by adding auxiliary variables and Lagrange multipliers. This Asymptotic-Preserving method generalizes the method investigated in a previous paper [arXiv:0903.4984v2] to the case of an arbitrary anisotropy direction field.

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Pierre Degond, Fabrice Deluzet, Alexei Lozinski, Jacek Narski, Claudia Negulescu. 2010-08-19. Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations. https://doi.org/10.4310/cms.2012.v10.n1.a2

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