Robin–Robin Domain Decomposition Methods for the Stokes–Darcy Coupling

Abstract

In this paper we consider a coupled system made of the 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.