TY - JOUR
T1 - A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations
AU - Li , Guanrong
AU - Chen , Yanping
AU - Huang , Yunqing
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 68
EP - 90
PY - 2022
DA - 2022/02
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2020-0165
UR - https://global-sci.org/intro/article_detail/nmtma/20221.html
KW - Reaction-diffusion equations, singular perturbation, modified weak Galerkin, finite element methods, discrete gradient.
AB - <p style="text-align: justify;">In this paper, a robust modified weak Galerkin (MWG) finite element
method for reaction-diffusion equations is proposed and investigated. An advantage
of this method is that it can deal with the singularly perturbed reaction-diffusion
equations. Another advantage of this method is that it produces fewer degrees of
freedom than the traditional WG method by eliminating the element boundaries
freedom. It is worth pointing out that, in our method, the test functions space is the
same as the finite element space, which is helpful for the error analysis. Optimal-order error estimates are established for the corresponding numerical approximation
in various norms. Some numerical results are reported to confirm the theory.</p>