Robust preconditioning for an HDG discretization of the time-dependent Stokes equations
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.
Keywords
Cite
@article{arxiv.2604.07202,
title = {Robust preconditioning for an HDG discretization of the time-dependent Stokes equations},
author = {Esteban Henríquez and Jeonghun J. Lee and Sander Rhebergen},
journal= {arXiv preprint arXiv:2604.07202},
year = {2026}
}