Robust preconditioning for an HDG discretization of the time-dependent Stokes equations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910113232584704 |
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| author | Henríquez, Esteban Lee, Jeonghun J. Rhebergen, Sander |
| author_facet | Henríquez, Esteban Lee, Jeonghun J. Rhebergen, Sander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07202 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust preconditioning for an HDG discretization of the time-dependent Stokes equations Henríquez, Esteban Lee, Jeonghun J. Rhebergen, Sander Numerical Analysis 65F08, 65M60, 76D07 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. |
| title | Robust preconditioning for an HDG discretization of the time-dependent Stokes equations |
| topic | Numerical Analysis 65F08, 65M60, 76D07 |
| url | https://arxiv.org/abs/2604.07202 |