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Coupling Stokes and Darcy equations. (English) Zbl 1134.76033
Summary: We study an interface problem between a fluid flow governed by Stokes equations, and a flow in a porous medium, governed by Darcy equations. We consider a weak formulation of the coupled problem which allows to use classical Stokes finite elements in the fluid domain, and standard continuous piecewise polynomials in the porous medium domain. Meshes do not need to match at the interface. The formulation of Stokes equations is standard, while a Galerkin least-squares formulation is used for a mixed form of Darcy equations. We prove the well-posedness of the coupled problem for this formulation and the convergence for some finite element approximations. We also give a two-dimensional numerical example.
MSC:
76M10Finite element methods (fluid mechanics)
76D07Stokes and related (Oseen, etc.) flows
76S05Flows in porous media; filtration; seepage