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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.
MSC:
76M10Finite element methods (fluid mechanics)
76S05Flows in porous media; filtration; seepage
76D07Stokes and related (Oseen, etc.) flows