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arXiv · 2604.07202

Robust preconditioning for an HDG discretization of the time-dependent Stokes equations

Esteban Henríquez·Jeonghun J. Lee·Sander Rhebergen
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Abstract

We present parameter-robust preconditioners for linear systems that arise after applying static condensation to a hybridizable discontinuous Galerkin (HDG) discretization of the time-dependent Stokes problem. Building upon the theoretical framework introduced in our previous work [SIAM Journal on Scientific Computing, 47(6):A3212-A3238, 2025], we extend the analysis to derive new preconditioners that remain robust with respect to all physical and discretization parameters. The construction relies on first establishing uniform well-posedness of the HDG formulation (before static condensation) through appropriately defined norms. Based on this result, we identify sufficient conditions that a norm on the face space must satisfy to guarantee parameter-robustness of the resulting preconditioner for the statically condensed HDG system. Numerical experiments in two and three dimensions verify our theoretical results.

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Esteban Henríquez, Jeonghun J. Lee, Sander Rhebergen. 2026-04-08. Robust preconditioning for an HDG discretization of the time-dependent Stokes equations. https://arxiv.org/abs/2604.07202

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