TY - JOUR
T1 - A Weak Galerkin Finite Element Method for a $H({\rm curl})$-Elliptic Problem
AU - Peng , Jie
AU - Xie , Yingying
AU - Xu , Yage
AU - Zhong , Liuqiang
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1411
EP - 1429
PY - 2025
DA - 2025/07
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2023-0101
UR - https://global-sci.org/intro/article_detail/aamm/24286.html
KW - $H({\rm curl})$-elliptic problem, weak Galerkin finite element method, weak curl operator, error estimate.
AB - <p style="text-align: justify;">In this paper, we develop and analyze a weak Galerkin (WG) finite element
method for solving a $H({\rm curl})$-elliptic problem. With the aid of the weak curl operator
and a stabilizer term, we first design a WG discretization. Then, by using an auxiliary
problem and establishing an error equation, we achieve the optimal order error estimates in both the energy norm and $L^2$ norm for the WG method. At last, we report
some numerical experiments to confirm the theoretical results.</p>