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Volume 16, Issue 1
Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes

Xiu Ye & Shangyou Zhang

DOI: 10.4208/nmtma.OA-2022-0082

Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 230-241.

Published online: 2023-01

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  • Abstract

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.

  • Keywords

Finite element, weak Galerkin method, stabilizer free, rectangular mesh.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-16-230, author = {Ye , Xiu and Zhang , Shangyou}, title = {Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {1}, pages = {230--241}, abstract = {

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} }
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 -

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.

Xiu Ye & Shangyou Zhang. (2023). Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes. Numerical Mathematics: Theory, Methods and Applications. 16 (1). 230-241. doi:10.4208/nmtma.OA-2022-0082
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