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Robin-Robin domain decomposition methods for the Stokes-Darcy coupling. (English) Zbl 1139.76030
Summary: We consider a coupled system made of Stokes and Darcy equations, and we propose some iteration-by-subdomain methods based on Robin conditions on the interface. We prove the convergence of these algorithms, and for suitable finite element approximations we show that the rate of convergence is independent of the mesh size h. Special attention is paid to the optimization of the performance of the methods when both the kinematic viscosity ν of the fluid and the hydraulic conductivity tensor K of the porous medium are very small.
MSC:
76M10Finite element methods (fluid mechanics)
76D07Stokes and related (Oseen, etc.) flows
76S05Flows in porous media; filtration; seepage
65N55Multigrid methods; domain decomposition (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)