Coupling Stokes and Darcy equations

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 piecew...

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Bibliographic Details
Published in:Applied numerical mathematics 2008-05, Vol.58 (5), p.525-538
Main Authors: Urquiza, J.M., N'Dri, D., Garon, A., Delfour, M.C.
Format: Article
Language:English
Subjects:
Beavers–Joseph–Saffman interface condition
Darcy equations
Exact sciences and technology
Galerkin least-squares method
Mathematical analysis
Mathematics
Mixed finite elements
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Sciences and techniques of general use
Stokes equations
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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. A two-dimensional numerical example is also given.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2006.12.006