Preconditioning of a hybridizable discontinuous Galerkin method for the coupled Stokes--Darcy system
Numerical Analysis
2026-04-27 v1 Numerical Analysis
Abstract
We propose parameter-robust preconditioners for the statically condensed linear system arising from a hybridizable discontinuous Galerkin discretization of the coupled Stokes--Darcy system. The design strategy relies on first applying the operator-preconditioning framework [Numer. Linear Algebra Appl., 18(1):1--40, 2011] to construct a preconditioner for the non-condensed discretization. This is done by proving uniform well-posedness of the scheme. Next, we prove robustness of the resulting condensed preconditioner applied to the reduced linear system using the framework we proposed in [SIAM J. Sci. Comput., 47(6):A3212--A3238, 2025]. Numerical examples demonstrate robustness of the proposed preconditioners.
Keywords
Cite
@article{arxiv.2604.22641,
title = {Preconditioning of a hybridizable discontinuous Galerkin method for the coupled Stokes--Darcy system},
author = {Esteban Henríquez and Miroslav Kuchta and Jeonghun J. Lee and Sander Rhebergen},
journal= {arXiv preprint arXiv:2604.22641},
year = {2026}
}