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We consider the problem of iteratively solving large and sparse doublesaddle-point systems arising from the stationary Stokes-Darcy equations in twodimensions, discretized by the Marker-and-Cell (MAC) finite difference method.We analyze the eigenvalue distribution of a few ideal block preconditioners. Wethen derive practical preconditioners that are based on approximations of Schurcomplements that arise in a block decomposition of the double saddle-pointmatrix. We show that including the interface conditions in the preconditionersis key in the pursuit of scalability. Numerical results show good convergencebehavior of our preconditioned GMRES solver and demonstrate robustness of theproposed preconditioner with respect to the physical parameters of the problem.

Block Preconditioners for the Marker-and-Cell Discretization of the Stokes-Darcy Equations