TY - JOUR
T1 - Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes
AU - Ye , Xiu
AU - Zhang , Shangyou
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 230
EP - 241
PY - 2023
DA - 2023/01
SN - 16
DO - http://doi.org/10.4208/nmtma.OA-2022-0082
UR - https://global-sci.org/intro/article_detail/nmtma/21350.html
KW - Finite element, weak Galerkin method, stabilizer free, rectangular mesh.
AB - <p style="text-align: justify;">In this paper, we introduce a stabilizer free weak Galerkin (SFWG) finite
element method for second order elliptic problems on rectangular meshes. With
a special weak Gradient space, an order two superconvergence for the SFWG finite
element solution is obtained, in both $L^2$ and $H^1$ norms. A local post-process lifts
such a $P_k$ weak Galerkin solution to an optimal order $P_{k+2}$ solution. The numerical
results confirm the theory.</p>