Volume 12, Issue 4
A Hybridized Weak Galerkin Finite Element Method for Incompressible Stokes Equations

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 1012-1038.

Published online: 2019-06

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• Abstract

In this paper, a hybridized weak Galerkin (HWG) finite element method is proposed for solving incompressible Stokes equations. The finite element space of the proposed method is constructed simply by piecewise polynomials. The optimal convergence order can be achieved for velocity function both in $L^2$ norm and $H^1$ norm, pressure function in $H^1$ norm. Finally, a Schur complement is employed to reduce the degree of freedom in discrete problem. Numerical examples are presented to demonstrate the effectiveness of the hybridized weak Galerkin finite element method.

• Keywords

Hybridized weak Galerkin FEM, discrete weak gradient, incompressible Stokes equations.

65N15, 65N30, 76D07

xiuli16@mails.jl u.edu.cn (Xiuli Wang)

diql15@mails.jlu.edu.cn (Qilong Zhai)

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• TXT
@Article{NMTMA-12-1012, author = {Zhang , Qianru and Kuang , Haopeng and Wang , Xiuli and Zhai , Qilong}, title = {A Hybridized Weak Galerkin Finite Element Method for Incompressible Stokes Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {4}, pages = {1012--1038}, abstract = {

In this paper, a hybridized weak Galerkin (HWG) finite element method is proposed for solving incompressible Stokes equations. The finite element space of the proposed method is constructed simply by piecewise polynomials. The optimal convergence order can be achieved for velocity function both in $L^2$ norm and $H^1$ norm, pressure function in $H^1$ norm. Finally, a Schur complement is employed to reduce the degree of freedom in discrete problem. Numerical examples are presented to demonstrate the effectiveness of the hybridized weak Galerkin finite element method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0021}, url = {http://global-sci.org/intro/article_detail/nmtma/13213.html} }
TY - JOUR T1 - A Hybridized Weak Galerkin Finite Element Method for Incompressible Stokes Equations AU - Zhang , Qianru AU - Kuang , Haopeng AU - Wang , Xiuli AU - Zhai , Qilong JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 1012 EP - 1038 PY - 2019 DA - 2019/06 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0021 UR - https://global-sci.org/intro/article_detail/nmtma/13213.html KW - Hybridized weak Galerkin FEM, discrete weak gradient, incompressible Stokes equations. AB -

In this paper, a hybridized weak Galerkin (HWG) finite element method is proposed for solving incompressible Stokes equations. The finite element space of the proposed method is constructed simply by piecewise polynomials. The optimal convergence order can be achieved for velocity function both in $L^2$ norm and $H^1$ norm, pressure function in $H^1$ norm. Finally, a Schur complement is employed to reduce the degree of freedom in discrete problem. Numerical examples are presented to demonstrate the effectiveness of the hybridized weak Galerkin finite element method.

Qianru Zhang, Haopeng Kuang, Xiuli Wang & Qilong Zhai. (2019). A Hybridized Weak Galerkin Finite Element Method for Incompressible Stokes Equations. Numerical Mathematics: Theory, Methods and Applications. 12 (4). 1012-1038. doi:10.4208/nmtma.OA-2018-0021
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