@Article{CiCP-18-1,
author = {},
title = {Discrete Maximum Principle for the Weak Galerkin Method for Anisotropic Diffusion Problems},
journal = {Communications in Computational Physics},
year = {2015},
volume = {18},
number = {1},
pages = {65--90},
abstract = {<p style="text-align: justify;">A weak Galerkin discretization of the boundary value problem of a general
anisotropic diffusion problem is studied for preservation of the maximum principle. It
is shown that the direct application of the M-matrix theory to the stiffness matrix of the
weak Galerkin discretization leads to a strong mesh condition requiring all of the mesh
dihedral angles to be strictly acute (a constant-order away from 90 degrees). To avoid
this difficulty, a reduced system is considered and shown to satisfy the discrete maximum
principle under weaker mesh conditions. The discrete maximum principle is
then established for the full weak Galerkin approximation using the relations between
the degrees of freedom located on elements and edges. Sufficient mesh conditions
for both piecewise constant and general anisotropic diffusion matrices are obtained.
These conditions provide a guideline for practical mesh generation for preservation of
the maximum principle. Numerical examples are presented.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.180914.121214a},
url = {https://global-sci.com/article/80310/discrete-maximum-principle-for-the-weak-galerkin-method-for-anisotropic-diffusion-problems}
}