Augmented interface systems for the Darcy-Stokes problem

In this paper we study interface equations associated to the Darcy-Stokes problem using the classical Steklov-Poincaré approach and a new one called augmented. We compare these two families of methods and characterize at the discrete level suitable preconditioners with additive and multiplicative structures. Finally, we present some numerical results to assess their behavior in presence of small physical parameters.