A Class of Weak Galerkin Finite Element Methods for the Incompressible Fluid Model

A Class of Weak Galerkin Finite Element Methods for the Incompressible Fluid Model

Year:    2019

Author:    Xiuli Wang, Qilong Zhai, Xiaoshen Wang

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0115

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 360–380

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

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

Author Details

Xiuli Wang

Qilong Zhai

Xiaoshen Wang