Parameter-Robust Preconditioner for Stokes-Darcy Coupled Problem with Lagrange Multiplier
Abstract
Abstract. In this paper, we propose a parameter-robust preconditioner for the coupled Stokes–Darcy problem equipped with various boundary conditions, enforcing the mass conservation at the interface via a Lagrange multiplier. We rigorously establish that the coupled system is well-posed with respect to physical parameters and mesh size and provides a framework for constructing parameter-robust preconditioners. Furthermore, we analyze the convergence behavior of the minimal residual method in the presence of small outlier eigenvalues linked to specific boundary conditions, which can lead to slow convergence or stagnation. To address this issue, we employ deflation techniques to accelerate the convergence. Finally, numerical experiments confirm the effectiveness and robustness of the proposed approach.
Fields of Study & Subjects
Matrix Theory and Algorithms
Advanced Numerical Methods in Computational Mathematics
Advanced Optimization Algorithms Research
Publication details
- Journal / source
- SIAM Journal on Scientific Computing
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 48
- Issue
- 2
- Pages
- A878–A904
- Publication date
- 9 April 2026
- Language
- EN