  We consider a coupled model of free-flow and porous medium flow, governed by
stationary Stokes and Darcy flow, respectively. The coupling between the two
systems is enforced by introducing a single variable representing the normal
flux across the interface. The problem is reduced to a system concerning only
the interface flux variable, which is shown to be well-posed in appropriately
weighted norms. An iterative solution scheme is then proposed to solve the
reduced problem such that mass is conserved at each iteration. By introducing a
preconditioner based on the weighted norms from the analysis, the performance
of the iterative scheme is shown to be robust with respect to material and
discretization parameters. By construction, the scheme is applicable to a wide
range of locally conservative discretization schemes and we consider explicit
examples in the framework of Mixed Finite Element methods. Finally, the
theoretical results are confirmed with the use of numerical experiments.
