  We propose an augmented Lagrangian-based preconditioner to accelerate the
convergence of Krylov subspace methods applied to linear systems of equations
with a block three-by-three structure such as those arising from mixed finite
element discretizations of the coupled Stokes-Darcy flow problem. We analyze
the spectrum of the preconditioned matrix and we show how the new
preconditioner can be efficiently applied. Numerical experiments are reported
to illustrate the effectiveness of the preconditioner in conjunction with
flexible GMRES for solving linear systems of equations arising from a 3D test
problem.
