Volume 17, Issue 5
The Weak Galerkin Finite Element Method for Solving the Time-Dependent Stokes Flow

Int. J. Numer. Anal. Mod., 17 (2020), pp. 732-745.

Published online: 2020-08

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• Abstract

In this paper, we solve the time-dependent Stokes problem by the weak Galerkin (WG) finite element method. Full-discrete WG finite element scheme is obtained by applying the implicit backward Euler method for time discretization. Optimal order error estimates are established for the corresponding numerical approximation in $H$1 norm for the velocity, and $L$2 norm for both the velocity and the pressure in semi-discrete forms and full-discrete forms, respectively. Some computational results are presented to demonstrate the accuracy, convergence and efficiency of the method.

• Keywords

Stokes problem, weak Galerkin finite element method, discrete weak gradient, discrete weak divergence.

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@Article{IJNAM-17-732, author = {Wang , Xiuli and LIiu , Yuanyuan and Zhai , Qilong}, title = {The Weak Galerkin Finite Element Method for Solving the Time-Dependent Stokes Flow}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {5}, pages = {732--745}, abstract = {

In this paper, we solve the time-dependent Stokes problem by the weak Galerkin (WG) finite element method. Full-discrete WG finite element scheme is obtained by applying the implicit backward Euler method for time discretization. Optimal order error estimates are established for the corresponding numerical approximation in $H$1 norm for the velocity, and $L$2 norm for both the velocity and the pressure in semi-discrete forms and full-discrete forms, respectively. Some computational results are presented to demonstrate the accuracy, convergence and efficiency of the method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/17877.html} }
TY - JOUR T1 - The Weak Galerkin Finite Element Method for Solving the Time-Dependent Stokes Flow AU - Wang , Xiuli AU - LIiu , Yuanyuan AU - Zhai , Qilong JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 732 EP - 745 PY - 2020 DA - 2020/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/17877.html KW - Stokes problem, weak Galerkin finite element method, discrete weak gradient, discrete weak divergence. AB -

In this paper, we solve the time-dependent Stokes problem by the weak Galerkin (WG) finite element method. Full-discrete WG finite element scheme is obtained by applying the implicit backward Euler method for time discretization. Optimal order error estimates are established for the corresponding numerical approximation in $H$1 norm for the velocity, and $L$2 norm for both the velocity and the pressure in semi-discrete forms and full-discrete forms, respectively. Some computational results are presented to demonstrate the accuracy, convergence and efficiency of the method.

Xiuli Wang, Yuanyuan LIiu & Qilong Zhai. (2020). The Weak Galerkin Finite Element Method for Solving the Time-Dependent Stokes Flow. International Journal of Numerical Analysis and Modeling. 17 (5). 732-745. doi:
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