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Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem

Weak Galerkin and Continuous Galerkin Coupled Finite Element Methods for the Stokes-Darcy Interface Problem
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Year:    2020

Author:    Hui Peng, Qilong Zhai, Ran Zhang, Shangyou Zhang

Communications in Computational Physics, Vol. 28 (2020), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2019-0122

Communications in Computational Physics, Vol. 28 (2020), Iss. 3 : pp. 1147–1175

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

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

Author Details

Hui Peng

Qilong Zhai

Ran Zhang

Shangyou Zhang

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