Numerical discretizations of a convective Brinkman-Forchheimer model under singular forcing
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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_ | 1866911780888903680 |
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| author | Allendes, Alejandro Campaña, Gilberto Otarola, Enrique |
| author_facet | Allendes, Alejandro Campaña, Gilberto Otarola, Enrique |
| contents | In two-dimensional Lipschitz domains, we analyze a Brinkman--Darcy--Forchheimer problem on the weighted spaces $\mathbf{H}_0^1(ω,Ω) \times L^2(ω,Ω)/\mathbb{R}$, where $ω$ belongs to the Muckenhoupt class $A_2$. Under a suitable smallness assumption, we prove the existence and uniqueness of a solution. We propose a finite element method and obtain a quasi-best approximation result in the energy norm \emph{à la Céa} under the assumption that $Ω$ is convex. We also develop an a posteriori error estimator and study its reliability and efficiency properties. Finally, we develop an adaptive method that yields optimal experimental convergence rates for the numerical examples we perform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_04427 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Numerical discretizations of a convective Brinkman-Forchheimer model under singular forcing Allendes, Alejandro Campaña, Gilberto Otarola, Enrique Numerical Analysis In two-dimensional Lipschitz domains, we analyze a Brinkman--Darcy--Forchheimer problem on the weighted spaces $\mathbf{H}_0^1(ω,Ω) \times L^2(ω,Ω)/\mathbb{R}$, where $ω$ belongs to the Muckenhoupt class $A_2$. Under a suitable smallness assumption, we prove the existence and uniqueness of a solution. We propose a finite element method and obtain a quasi-best approximation result in the energy norm \emph{à la Céa} under the assumption that $Ω$ is convex. We also develop an a posteriori error estimator and study its reliability and efficiency properties. Finally, we develop an adaptive method that yields optimal experimental convergence rates for the numerical examples we perform. |
| title | Numerical discretizations of a convective Brinkman-Forchheimer model under singular forcing |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2305.04427 |