Parameter-Robust Preconditioners for the Stokes–Darcy Coupled Problem without Fractional Operators

Abstract.

We consider the Stokes–Darcy coupled problem, which models the interaction between free flow and porous medium flow. By enforcing the normal flux continuity interface condition directly within the finite-element space, we establish unified well-posedness results for the coupled system under various boundary condition scenarios. Using the operator preconditioning framework, we develop a parameter-robust preconditioner that avoids the use of fractional operators. Numerical experiments employing both [Formula: see text]-conforming and nonconforming finite-element methods are presented to confirm the theoretical findings and demonstrate the robustness of the proposed block preconditioner with respect to the physical parameters and mesh size.

Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/xuesdu/SD.git and in the supplementary materials ( SD-master.zip [341KB]). [Formula: see text]