TY - JOUR
T1 - Analysis of Weak Galerkin Finite Element Methods with Supercloseness 
AU - AL-Taweel , Ahmed
AU - Hussain , Saqib
AU - Wang , Xiaoshen
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 761
EP - 776
PY - 2022
DA - 2022/09
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/21032.html
KW - Weak Galerkin, finite element methods, weak gradient, second-order elliptic problems, supercloseness, superconvergence.
AB - <p style="text-align: justify;">In [15], the computational performance of various weak Galerkin finite element methods in terms of stability, convergence, and supercloseness is explored and numerical results are listed in 31 tables. Some of the phenomena can be explained by the existing theoretical results and the others are to be explained. The main purpose of this paper is to provide a unified theoretical foundation to a class of WG schemes, where $(P_k(T), P_{k+1}(e), [P_{k+1}(T)]^2)$ elements are used for solving the second order elliptic equations (1)-(2) on a triangle grid in 2D. With this unified treatment, all of the existing results become special cases. The theoretical conclusions are corroborated by a number of numerical examples.</p>