Volume 28, Issue 3
Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem

Hui Peng, Qilong Zhai, Ran Zhang & Shangyou Zhang

Commun. Comput. Phys., 28 (2020), pp. 1147-1175.

Published online: 2020-07

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  • Abstract

We consider a model of coupled free and porous media flow governed by Stokes equation and Darcy's law with the Beavers-Joseph-Saffman interface condition. In this paper, we propose a new numerical approach for the Stokes-Darcy system. The approach employs the classical finite element method for the Darcy region and the weak Galerkin finite element method for the Stokes region. We construct corresponding discrete scheme and prove its well-posedness. The estimates for the corresponding numerical approximation are derived. Finally, we present some numerical experiments to validate the efficiency of the approach for solving this problem.

  • Keywords

Finite element methods, weak Galerkin finite element methods, weak gradient, Stokes equations, Darcy's equation.

  • AMS Subject Headings

65N30, 65N15, 65N12, 74N20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-1147, author = {Hui Peng , and Qilong Zhai , and Ran Zhang , and Shangyou Zhang , }, title = {Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {3}, pages = {1147--1175}, abstract = {

We consider a model of coupled free and porous media flow governed by Stokes equation and Darcy's law with the Beavers-Joseph-Saffman interface condition. In this paper, we propose a new numerical approach for the Stokes-Darcy system. The approach employs the classical finite element method for the Darcy region and the weak Galerkin finite element method for the Stokes region. We construct corresponding discrete scheme and prove its well-posedness. The estimates for the corresponding numerical approximation are derived. Finally, we present some numerical experiments to validate the efficiency of the approach for solving this problem.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0122}, url = {http://global-sci.org/intro/article_detail/cicp/17689.html} }
TY - JOUR T1 - Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem AU - Hui Peng , AU - Qilong Zhai , AU - Ran Zhang , AU - Shangyou Zhang , JO - Communications in Computational Physics VL - 3 SP - 1147 EP - 1175 PY - 2020 DA - 2020/07 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2019-0122 UR - https://global-sci.org/intro/article_detail/cicp/17689.html KW - Finite element methods, weak Galerkin finite element methods, weak gradient, Stokes equations, Darcy's equation. AB -

We consider a model of coupled free and porous media flow governed by Stokes equation and Darcy's law with the Beavers-Joseph-Saffman interface condition. In this paper, we propose a new numerical approach for the Stokes-Darcy system. The approach employs the classical finite element method for the Darcy region and the weak Galerkin finite element method for the Stokes region. We construct corresponding discrete scheme and prove its well-posedness. The estimates for the corresponding numerical approximation are derived. Finally, we present some numerical experiments to validate the efficiency of the approach for solving this problem.

Hui Peng, Qilong Zhai, Ran Zhang & Shangyou Zhang. (2020). Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem. Communications in Computational Physics. 28 (3). 1147-1175. doi:10.4208/cicp.OA-2019-0122
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