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Volume 11, Issue 2
A Class of Weak Galerkin Finite Element Methods for the Incompressible Fluid Model

Xiuli Wang, Qilong Zhai & Xiaoshen Wang

Adv. Appl. Math. Mech., 11 (2019), pp. 360-380.

Published online: 2019-01

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  • Abstract

In this paper, we propose a weak Galerkin finite element method (WG) for solving the stationary incompressible Stokes equation in two or three dimensional space. The weak Galerkin finite element method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape regularity. However, since additional variables are introduced, the computational cost is much higher. Our new method can significantly reduce the computational cost  while maintaining the accuracy. Optimal error orders are established for the weak Galerkin finite element approximations in various norms. Some numerical results are presented to demonstrate the efficiency of the method.

  • AMS Subject Headings

65N15, 65N30, 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-360, author = {Wang , XiuliZhai , Qilong and Wang , Xiaoshen}, title = {A Class of Weak Galerkin Finite Element Methods for the Incompressible Fluid Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {2}, pages = {360--380}, abstract = {

In this paper, we propose a weak Galerkin finite element method (WG) for solving the stationary incompressible Stokes equation in two or three dimensional space. The weak Galerkin finite element method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape regularity. However, since additional variables are introduced, the computational cost is much higher. Our new method can significantly reduce the computational cost  while maintaining the accuracy. Optimal error orders are established for the weak Galerkin finite element approximations in various norms. Some numerical results are presented to demonstrate the efficiency of the method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0115}, url = {http://global-sci.org/intro/article_detail/aamm/12967.html} }
TY - JOUR T1 - A Class of Weak Galerkin Finite Element Methods for the Incompressible Fluid Model AU - Wang , Xiuli AU - Zhai , Qilong AU - Wang , Xiaoshen JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 360 EP - 380 PY - 2019 DA - 2019/01 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0115 UR - https://global-sci.org/intro/article_detail/aamm/12967.html KW - Incompressible Stokes equation, weak Galerkin finite element method, discrete weak gradient, Schur complement. AB -

In this paper, we propose a weak Galerkin finite element method (WG) for solving the stationary incompressible Stokes equation in two or three dimensional space. The weak Galerkin finite element method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape regularity. However, since additional variables are introduced, the computational cost is much higher. Our new method can significantly reduce the computational cost  while maintaining the accuracy. Optimal error orders are established for the weak Galerkin finite element approximations in various norms. Some numerical results are presented to demonstrate the efficiency of the method.

Xiuli Wang, Qilong Zhai & Xiaoshen Wang. (2020). A Class of Weak Galerkin Finite Element Methods for the Incompressible Fluid Model. Advances in Applied Mathematics and Mechanics. 11 (2). 360-380. doi:10.4208/aamm.OA-2018-0115
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