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arXiv · 2604.22641

Preconditioning of a hybridizable discontinuous Galerkin method for the coupled Stokes--Darcy system

Esteban Henríquez·Miroslav Kuchta·Jeonghun J. Lee·Sander Rhebergen
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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.

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Esteban Henríquez, Miroslav Kuchta, Jeonghun J. Lee, Sander Rhebergen. 2026-04-24. Preconditioning of a hybridizable discontinuous Galerkin method for the coupled Stokes--Darcy system. https://arxiv.org/abs/2604.22641

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