TY - JOUR
T1 - Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems
AU - Chen , Xingding
AU - Yuan , Guangwei
AU - Yu , Yunlong
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 849
EP - 866
PY - 2014
DA - 2014/06
SN - 6
DO - http://doi.org/10.4208/aamm.2013.m445
UR - https://global-sci.org/intro/article_detail/aamm/52.html
KW - Discrete maximum principle, finite element scheme, repair technique, anisotropic
diffusion problems.
AB - <p style="text-align: justify;">In this paper, we construct a global repair technique for the finite element scheme of
anisotropic diffusion equations to enforce the repaired solutions satisfying
the discrete maximum principle. It is an extension of the existing local
repair technique. Both of the repair techniques
preserve the total energy and are easy to be implemented. The numerical
experiments show that these repair techniques do not destroy the accuracy
of the finite element scheme, and the computational cost of the
global repair technique is lower than the local repair technique when the
diffusion tensors are highly anisotropic.</p>