Finite element approximation for a convective Brinkman--Forchheimer problem coupled with a heat equation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916488306229248 |
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| author | Campaña, Gilberto Muñoz, Pablo Otarola, Enrique |
| author_facet | Campaña, Gilberto Muñoz, Pablo Otarola, Enrique |
| contents | We investigate a convective Brinkman--Forchheimer problem coupled with a heat equation. The investigated model considers thermal diffusion and viscosity depending on the temperature. We prove the existence of a solution without restriction on the data and uniqueness when the solution is slightly smoother and the data is suitably restricted. We also propose a finite element discretization scheme for the considered model and derive convergence results and a priori error estimates. Finally, we illustrate the theory with numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09872 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite element approximation for a convective Brinkman--Forchheimer problem coupled with a heat equation Campaña, Gilberto Muñoz, Pablo Otarola, Enrique Numerical Analysis We investigate a convective Brinkman--Forchheimer problem coupled with a heat equation. The investigated model considers thermal diffusion and viscosity depending on the temperature. We prove the existence of a solution without restriction on the data and uniqueness when the solution is slightly smoother and the data is suitably restricted. We also propose a finite element discretization scheme for the considered model and derive convergence results and a priori error estimates. Finally, we illustrate the theory with numerical examples. |
| title | Finite element approximation for a convective Brinkman--Forchheimer problem coupled with a heat equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2403.09872 |