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.


76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
76D07 Stokes and related (Oseen, etc.) flows
86A05 Hydrology, hydrography, oceanography


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