Robust finite element methods and solvers for the Biot--Brinkman equations in vorticity form
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866915568056008704 |
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| author | Caraballo, Ruben In, Chansophea Wathanak Martín, Alberto F. Ruiz-Baier, Ricardo |
| author_facet | Caraballo, Ruben In, Chansophea Wathanak Martín, Alberto F. Ruiz-Baier, Ricardo |
| contents | In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of parameter-weighted spaces, which allows for a more accurate and robust analysis of the continuous and discrete problems. Furthermore, we conduct a solvability analysis of the proposed method and derive optimal error estimates in appropriate norms. These error estimates are shown to be robust in the case of large Lamé parameters and small permeability and storativity coefficients. To illustrate the effectiveness of the proposed method, we provide a few representative numerical examples, including convergence verification, poroelastic channel flow simulation, and test the robustness of block-diagonal preconditioners with respect to model parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Robust finite element methods and solvers for the Biot--Brinkman equations in vorticity form Caraballo, Ruben In, Chansophea Wathanak Martín, Alberto F. Ruiz-Baier, Ricardo Numerical Analysis 65N30, 65N15, 76S05, 35Q74 In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of parameter-weighted spaces, which allows for a more accurate and robust analysis of the continuous and discrete problems. Furthermore, we conduct a solvability analysis of the proposed method and derive optimal error estimates in appropriate norms. These error estimates are shown to be robust in the case of large Lamé parameters and small permeability and storativity coefficients. To illustrate the effectiveness of the proposed method, we provide a few representative numerical examples, including convergence verification, poroelastic channel flow simulation, and test the robustness of block-diagonal preconditioners with respect to model parameters. |
| title | Robust finite element methods and solvers for the Biot--Brinkman equations in vorticity form |
| topic | Numerical Analysis 65N30, 65N15, 76S05, 35Q74 |
| url | https://arxiv.org/abs/2307.01484 |