Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations. (English) Zbl 1170.76024

Summary: We consider the coupling across an interface of fluid and porous medium flows with Beavers-Joseph-Saffman transmission conditions. Under an adequate choice of Lagrange multipliers on the interface, we analyze inf-sup conditions and optimal a priori error estimates associated with continuous and discrete formulations of this Stokes-Darcy system. We allow the meshes of the two regions to be non-matching across the interface. Using mortar finite element analysis and appropriate scaled norms, we show that the constants that appear in a priori error bounds do not depend on viscosity, permeability and ratio of mesh parameters. Numerical experiments are presented.


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