Parameter-robust Preconditioners for the Stokes-Darcy Coupled Problem without Fractional Operators
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915399462813696 |
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| author | Boon, Wietse M. Hu, Xiaozhe Wang, Xue |
| author_facet | Boon, Wietse M. Hu, Xiaozhe Wang, Xue |
| contents | We consider the Stokes-Darcy coupled problem, which models the interaction between free-flow and porous medium flow. By enforcing the normal flux continuity interface condition directly within the finite-element spaces, we establish unified well-posedness results for the coupled system under various boundary condition scenarios. Using the operator preconditioning framework, we develop a parameter-robust preconditioner that avoids the use of fractional operators. Numerical experiments employing both $H(\operatorname{div})$-conforming and nonconforming finite-element methods are presented to confirm the theoretical findings and demonstrate the robustness of the proposed block preconditioners with respect to the physical parameters and mesh size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parameter-robust Preconditioners for the Stokes-Darcy Coupled Problem without Fractional Operators Boon, Wietse M. Hu, Xiaozhe Wang, Xue Numerical Analysis We consider the Stokes-Darcy coupled problem, which models the interaction between free-flow and porous medium flow. By enforcing the normal flux continuity interface condition directly within the finite-element spaces, we establish unified well-posedness results for the coupled system under various boundary condition scenarios. Using the operator preconditioning framework, we develop a parameter-robust preconditioner that avoids the use of fractional operators. Numerical experiments employing both $H(\operatorname{div})$-conforming and nonconforming finite-element methods are presented to confirm the theoretical findings and demonstrate the robustness of the proposed block preconditioners with respect to the physical parameters and mesh size. |
| title | Parameter-robust Preconditioners for the Stokes-Darcy Coupled Problem without Fractional Operators |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.06369 |