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Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes

Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes

Year:    2023

Author:    Xiu Ye, Shangyou Zhang

Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 1 : pp. 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 L2 and H1 norms. A local post-process lifts such a Pk weak Galerkin solution to an optimal order Pk+2 solution. The numerical results confirm the theory.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2022-0082

Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 1 : pp. 230–241

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Finite element weak Galerkin method stabilizer free rectangular mesh.

Author Details

Xiu Ye

Shangyou Zhang

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