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We consider a coupled model of free-flow and porous medium flow, governed bystationary Stokes and Darcy flow, respectively. The coupling between the twosystems is enforced by introducing a single variable representing the normalflux across the interface. The problem is reduced to a system concerning onlythe interface flux variable, which is shown to be well-posed in appropriatelyweighted norms. An iterative solution scheme is then proposed to solve thereduced problem such that mass is conserved at each iteration. By introducing apreconditioner based on the weighted norms from the analysis, the performanceof the iterative scheme is shown to be robust with respect to material anddiscretization parameters. By construction, the scheme is applicable to a widerange of locally conservative discretization schemes and we consider explicitexamples in the framework of Mixed Finite Element methods. Finally, thetheoretical results are confirmed with the use of numerical experiments.

A Parameter-Robust Iterative Method for Stokes-Darcy Problems Retaining Local Mass Conservation