Preconditioning of a hybridizable discontinuous Galerkin method for the coupled Stokes--Darcy system
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911621583994880 |
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| author | Henríquez, Esteban Kuchta, Miroslav Lee, Jeonghun J. Rhebergen, Sander |
| author_facet | Henríquez, Esteban Kuchta, Miroslav Lee, Jeonghun J. Rhebergen, Sander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22641 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Preconditioning of a hybridizable discontinuous Galerkin method for the coupled Stokes--Darcy system Henríquez, Esteban Kuchta, Miroslav Lee, Jeonghun J. Rhebergen, Sander Numerical Analysis 65F08, 65N30, 76D07, 76S99 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. |
| title | Preconditioning of a hybridizable discontinuous Galerkin method for the coupled Stokes--Darcy system |
| topic | Numerical Analysis 65F08, 65N30, 76D07, 76S99 |
| url | https://arxiv.org/abs/2604.22641 |