On classical iterative subdomain methods for the Stokes-Darcy problem

Within classical iterative subdomain methods, the problems in the subdomains are solved alternately by only using data on the interface provided from the other subdomains. Methods of this type for the Stokes-Darcy problem that use Robin boundary conditions on the interface are reviewed. Their common underlying structure and their main differences are identified. In particular, it is clarified that there are different updating strategies for the interface conditions. For small values of fluid viscosity and hydraulic permeability, which are relevant in applications from geosciences, it is shown in numerical studies that only one of these updating strategies leads to an efficient numerical method, if it is used with appropriate parameters in the Robin conditions.