TY - JOUR
T1 - A Modified Weak Galerkin Finite Element Method for Singularly Perturbed Parabolic Convection-Diffusion-Reaction Problems
AU - Toprakseven , Suayip
AU - Gao , Fuzheng
JO - Journal of Computational Mathematics
VL - 6
SP - 1246
EP - 1280
PY - 2023
DA - 2023/11
SN - 41
DO - http://doi.org/10.4208/jcm.2203-m2021-0031
UR - https://global-sci.org/intro/article_detail/jcm/22111.html
KW - The modified weak Galerkin finite element method, Backward Euler method, Parabolic convection-diffusion problems, Error estimates.
AB - <p style="text-align: justify;">In this work, a modified weak Galerkin finite element method is proposed for solving
second order linear parabolic singularly perturbed convection-diffusion equations. The
key feature of the proposed method is to replace the classical gradient and divergence
operators by the modified weak gradient and modified divergence operators, respectively.
We apply the backward finite difference method in time and the modified weak Galerkin
finite element method in space on uniform mesh. The stability analyses are presented
for both semi-discrete and fully-discrete modified weak Galerkin finite element methods.
Optimal order of convergences are obtained in suitable norms. We have achieved the same
accuracy with the weak Galerkin method while the degrees of freedom are reduced in our
method. Various numerical examples are presented to support the theoretical results. It
is theoretically and numerically shown that the method is quite stable.</p>