Finite element approximations for Stokes-Darcy flow with Beavers-Joseph interface conditions. (English) Zbl 1252.76040

Cao, Yanzhao; Gunzburger, Max; Hu, Xiaolong; Hua, Fei; Wang, Xiaoming; Zhao, Weidong

SIAM J. Numer. Anal. 47, No. 6, 4239-4256 (2010).

Summary: 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.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76D07	Stokes and related (Oseen, etc.) flows
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q35	PDEs in connection with fluid mechanics
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs

Keywords:

Stokes and Darcy equations; finite element approximation; error bound; initial-boundary value problem; fluid and porous media flow; Beavers-Joseph interface boundary condition