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