A BFBt preconditioner for double saddle-point systems

We consider block preconditioners for double saddle-point systems and investigate the effect of approximating the nested Schur complement associated with the trailing diagonal block on the eigenvalue distribution of the preconditioned matrix. We develop a variant of Elman’s BFBt method and adapt it to this family of linear systems. Our findings are illustrated on a Marker-and-Cell discretization of the Stokes–Darcy equations.