Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 230-241.
Published online: 2023-01
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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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0082}, url = {http://global-sci.org/intro/article_detail/nmtma/21350.html} }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.