Robin-Robin domain decomposition methods for the Stokes-Darcy coupling. (English) Zbl 1139.76030

Discacciati, Marco; Quarteroni, Alfio; Valli, Alberto

SIAM J. Numer. Anal. 45, No. 3, 1246-1268 (2007).

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 applied to problems in fluid mechanics
76D07	Stokes and related (Oseen, etc.) flows
76S05	Flows in porous media; filtration; seepage
65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

Robin interface condition; finite element approximation; convergence