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.


  • Keywords

Incompressible Stokes equation weak Galerkin finite element method discrete weak gradient Schur complement.

  • AMS Subject Headings

65N15 65N30 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-360, author = {Xiuli Wang, Qilong Zhai and Xiaoshen Wang}, 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} }
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