Discrete maximum principle and a Delaunay-type mesh condition for linear finite element approximations of two-dimensional anisotropic diffusion problems

Details Discrete maximum principle and a Delaunay-type mesh condition for linear finite element approximations of two-dimensional anisotropic diffusion problems Discrete maximum principle and a Delaunay-type mesh condition for linear finite element approximations of two-dimensional anisotropic diffusion problems

2010-08-03

arxiv.org/abs/1008.0562v1

Numerical Mathematics: Theory, Methods and Applications 4 (2011), 319-334

Mathematics

Numerical Analysis

16 pages

Scientific paper

The finite element solution of two-dimensional anisotropic diffusion problems is considered. A Delaunay-type mesh condition is developed for linear finite element approximations to satisfy a discrete maximum principle. The condition is shown to be weaker than the existing anisotropic non-obtuse angle condition. It reduces to the well known Delaunay condition for the special case with the identity diffusion matrix. Numerical results are presented to verify the theoretical findings.

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