Numerical analysis of the Navier-Stokes/Darcy coupling

We consider a differential system based on the coupling of the Navier– Stokes and Darcy equations for modeling the interaction between surface and porous-media flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov–Poincaré operators, and we prove its well-posedness. We propose and analyze iterative methods to solve a conforming finite element approximation of the coupled problem