Robust Monolithic Solvers for the Stokes--Darcy Problem with the Darcy Equation in Primal Form

Abstract

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 nonconforming 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.