Volume 4, Issue 3
Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

Weizhang Huang

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 319-334.

Published online: 2011-04

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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

Anisotropic diffusion, discrete maximum principle, finite element, mesh generation, Delaunay triangulation, Delaunay condition.

  • AMS Subject Headings

65N30, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-319, author = {}, title = {Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {3}, pages = {319--334}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m1024}, url = {http://global-sci.org/intro/article_detail/nmtma/5971.html} }
TY - JOUR T1 - Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 319 EP - 334 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m1024 UR - https://global-sci.org/intro/article_detail/nmtma/5971.html KW - Anisotropic diffusion, discrete maximum principle, finite element, mesh generation, Delaunay triangulation, Delaunay condition. AB -

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.

Weizhang Huang. (2020). Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems. Numerical Mathematics: Theory, Methods and Applications. 4 (3). 319-334. doi:10.4208/nmtma.2011.m1024
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