  The coupled Darcy-Stokes problem is widely used for modeling fluid transport
in physical systems consisting of a porous part and a free part. In this work
we consider preconditioners for monolitic solution algorithms of the coupled
Darcy-Stokes problem, where the Darcy problem is in primal form. We employ the
operator preconditioning framework and utilize a fractional solver at the
interface between the problems to obtain order optimal schemes that are robust
with respect to the material parameters, i.e. the permeability, viscosity and
Beavers-Joseph-Saffman parameter. Our approach is similar to our earlier work,
but since the Darcy problem is in primal form, the mass conservation at the
interface introduces some challenges. These challenges will be specifically
addressed in this paper. Numerical experiments illustrating the performance are
provided. The preconditioner is posed in non-standard Sobolev spaces which may
be perceived as an obstacle for its use in applications. However, we detail the
implementational aspects and show that the preconditioner is quite feasible to
realize in practice.
