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.
@article{arxiv.2110.07486,
title = {Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form},
author = {Wietse M. Boon and Timo Koch and Miroslav Kuchta and Kent-Andre Mardal},
journal= {arXiv preprint arXiv:2110.07486},
year = {2021}
}