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Mortar finite element discretization of a model coupling Darcy and Stokes equations. (English) Zbl 1138.76044
Summary: As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where Darcy and Stokes equations are coupled via appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the flow inside and outside the porous medium. We prove a priori and a posteriori error estimates for the resulting discrete problem. Some numerical experiments confirm the interest of the discretization.
MSC:
76M10Finite element methods (fluid mechanics)
76S05Flows in porous media; filtration; seepage
76D07Stokes and related (Oseen, etc.) flows
86A05Hydrology, hydrography, oceanography