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 - <p style="text-align: justify;">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.</p>