H(div) conforming finite element methods for the coupled Stokes and Darcy problem

Authors:
Yumei Chen;Feiteng Huang;Xiaoping Xie
Affiliations:
College of Mathematics and Information, China West Normal University, Nanchong 637009, China;School of Mathematics, Sichuan University, Chengdu 610064, China;School of Mathematics, Sichuan University, Chengdu 610064, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

This paper proposes and analyzes a numerical method for solving the coupled Stokes and Darcy problem, an interface problem between a fluid, governed by Stokes equations, and a flow in a porous medium, governed by Darcy equations. The method employs H(div) conforming finite elements for the velocity field in both Stokes and Darcy subdomains. Optimal-order error estimates are established.