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Locally conservative coupling of Stokes and Darcy flows. (English) Zbl 1084.35063
Summary: A locally conservative numerical method for solving the coupled Stokes and Darcy flows problem is formulated and analyzed. The approach employs the mixed finite element method for the Darcy region and the discontinuous Galerkin method for the Stokes region. A discrete inf-sup condition and optimal error estimates are derived.
MSC:
35Q35PDEs in connection with fluid mechanics
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
76D07Stokes and related (Oseen, etc.) flows
76S05Flows in porous media; filtration; seepage
76M10Finite element methods (fluid mechanics)