Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations
Numerical Analysis
2014-04-08 v1
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.
Keywords
Cite
@article{arxiv.1008.3405,
title = {Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations},
author = {Pierre Degond and Fabrice Deluzet and Alexei Lozinski and Jacek Narski and Claudia Negulescu},
journal= {arXiv preprint arXiv:1008.3405},
year = {2014}
}