full
search.png

Search

close.png

Cancel

arrow
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

DOI: 10.4208/nmtma.2011.m1024

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

Published online: 2011-04

Preview Full PDF 2884 32771

Cited by

google scholar semantic scholar
Export citation
  • 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

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-4-319, author = {Weizhang Huang}, 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 AU - Weizhang Huang 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. (2011). 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
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard