Finite Element Approximations for Stokes-Darcy Flow with Beavers-Joseph Interface Conditions

Authors:
Yanzhao Cao;Max Gunzburger;Xiaolong Hu;Fei Hua;Xiaoming Wang;Weidong Zhao
Affiliations:
yzc0009@auburn.edu;mgunzburger@fsu.edu;hu@gly.fsu.edu;fhua@math.fsu.edu;wxm@math.fsu.edu;wdzhao@sdu.edu.cn
Venue:
SIAM Journal on Numerical Analysis
Year:
2010

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Abstract

Numerical solutions using finite element methods are considered for transient flow in a porous medium coupled to free flow in embedded conduits. Such situations arise, for example, for groundwater flows in karst aquifers. The coupled flow is modeled by the Darcy equation in a porous medium and the Stokes equations in the conduit domain. On the interface between the matrix and conduit, Beavers-Joseph interface conditions, instead of the simplified Beavers-Joseph-Saffman conditions, are imposed. Convergence and error estimates for finite element approximations are obtained. Numerical experiments illustrate the validity of the theoretical results.