Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form

TL;DR

This paper develops mesh-independent, parameter-robust monolithic solvers for the coupled Stokes-Darcy problem, employing various discretizations and fractional Sobolev space-based preconditioners, with numerical validation of robustness.

Contribution

It introduces a unified framework for constructing robust preconditioners for multiple formulations of the Stokes-Darcy problem, enhancing solver stability and efficiency.

Findings

Preconditioners are mesh-independent and parameter-robust.

Numerical experiments confirm robustness across formulations.

Operators in fractional Sobolev spaces are effectively utilized.

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 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.