  We construct mesh-independent and parameter-robust monolithic solvers for the
coupled primal Stokes-Darcy problem. Three different formulations and their
discretizations in terms of conforming and non-conforming finite element
methods and finite volume methods are considered. In each case, robust
preconditioners are derived using a unified theoretical framework. In
particular, the suggested preconditioners utilize operators in fractional
Sobolev spaces. Numerical experiments demonstrate the parameter-robustness of
the proposed solvers.
