Volume 14, Issue 1
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations

Yue Feng, Yujie Liu, Ruishu Wang & Shangyou Zhang

Adv. Appl. Math. Mech., 14 (2022), pp. 181-201.

Published online: 2021-11

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  • Abstract

A stabilizer-free weak Galerkin finite element method is proposed for the Stokes equations in this paper. Here we omit the stabilizer term in the new method by increasing the degree of polynomial approximating spaces for the weak gradient operators. The new algorithm is simple in formulation and the computational complexity is also reduced. The corresponding approximating spaces consist of piecewise polynomials of degree $k\geq1$ for the velocity and $k-1$ for the pressure, respectively. Optimal order error estimates have been derived for the velocity in both $H^1$ and $L^2$ norms and for the pressure in $L^2$ norm. Numerical examples are presented to illustrate the accuracy and convergency of the method.

  • Keywords

Stokes equations, weak Galerkin finite element method, stabilizer free, discrete weak differential operators.

  • AMS Subject Headings

65N15, 65N30, 76D07, 35B45, 35J50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-181, author = {Feng , Yue and Liu , Yujie and Wang , Ruishu and Zhang , Shangyou}, title = {A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {14}, number = {1}, pages = {181--201}, abstract = {

A stabilizer-free weak Galerkin finite element method is proposed for the Stokes equations in this paper. Here we omit the stabilizer term in the new method by increasing the degree of polynomial approximating spaces for the weak gradient operators. The new algorithm is simple in formulation and the computational complexity is also reduced. The corresponding approximating spaces consist of piecewise polynomials of degree $k\geq1$ for the velocity and $k-1$ for the pressure, respectively. Optimal order error estimates have been derived for the velocity in both $H^1$ and $L^2$ norms and for the pressure in $L^2$ norm. Numerical examples are presented to illustrate the accuracy and convergency of the method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0325}, url = {http://global-sci.org/intro/article_detail/aamm/19981.html} }
TY - JOUR T1 - A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations AU - Feng , Yue AU - Liu , Yujie AU - Wang , Ruishu AU - Zhang , Shangyou JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 181 EP - 201 PY - 2021 DA - 2021/11 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0325 UR - https://global-sci.org/intro/article_detail/aamm/19981.html KW - Stokes equations, weak Galerkin finite element method, stabilizer free, discrete weak differential operators. AB -

A stabilizer-free weak Galerkin finite element method is proposed for the Stokes equations in this paper. Here we omit the stabilizer term in the new method by increasing the degree of polynomial approximating spaces for the weak gradient operators. The new algorithm is simple in formulation and the computational complexity is also reduced. The corresponding approximating spaces consist of piecewise polynomials of degree $k\geq1$ for the velocity and $k-1$ for the pressure, respectively. Optimal order error estimates have been derived for the velocity in both $H^1$ and $L^2$ norms and for the pressure in $L^2$ norm. Numerical examples are presented to illustrate the accuracy and convergency of the method.

Yue Feng, Yujie Liu, Ruishu Wang & Shangyou Zhang. (1970). A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations. Advances in Applied Mathematics and Mechanics. 14 (1). 181-201. doi:10.4208/aamm.OA-2020-0325
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