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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 $\nu$ of the fluid and the hydraulic conductivity tensor $K$ of the porous medium are very small.
##### MSC:
 76M10 Finite element methods (fluid mechanics) 76D07 Stokes and related (Oseen, etc.) flows 76S05 Flows in porous media; filtration; seepage 65N55 Multigrid methods; domain decomposition (BVP of PDE) 65N12 Stability and convergence of numerical methods (BVP of PDE) 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)