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Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

Published online by Cambridge University Press:  28 May 2015

Weizhang Huang
Weizhang Huang*
Affiliation:
Department of Mathematics, the University of Kansas, Lawrence, KS 66045, USA
*
*Corresponding author.Email address:huang@math.ku.edu
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Abstract

A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle. The condition is weaker than the existing anisotropic non-obtuse angle condition and 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.

Keywords

65N3065N50Anisotropic diffusiondiscrete maximum principlefinite elementmesh generationDelaunay triangulationDelaunay condition

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Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 3 , August 2011 , pp. 319 - 334
Copyright
Copyright © Global Science Press Limited 2011

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