DISCACCIATI, M. and QUARTERONI, A., 2003. Analysis of a domain decomposition method for the coupling of Stokes and Darcy equations. IN: Brezzi, F. ... et al (eds). Numerical Analysis and Advanced Applications: Proceedings of ENUMATH 2001 the 4th European Conference on Numerical Mathematics and Advanced Applications Ischia, July 2001. Milan: Springer Milan, pp.3-20.
We introduce a differential system based on the coupling of the (Navier) Stokes equations and the Darcy equation for the modelling of the interaction between surface and subsurface flows. We formulate the problem as an interface problem and analyze the associated Steklov-Poincaré operator. We then propose a way of solving the coupled problem iteratively, based on a suitable splitting of the interface conditions, allowing the solution of two subproblems at each step.