Numerical discretization of a Darcy-Forchheimer problem coupled with a singular heat equation
| Autor: | Allendes, Alejandro, Campaña, Gilberto, Otarola, Enrique |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | In Lipschitz domains, we study a Darcy-Forchheimer problem coupled with a singular heat equation by a nonlinear forcing term depending on the temperature. By singular we mean that the heat source corresponds to a Dirac measure. We establish the existence of solutions for a model that allows a diffusion coefficient in the heat equation depending on the temperature. For such a model, we also propose a finite element discretization scheme and provide an a priori convergence analysis. In the case that the aforementioned diffusion coefficient is constant, we devise an a posteriori error estimator and investigate reliability and efficiency properties. We conclude by devising an adaptive loop based on the proposed error estimator and presenting numerical experiments. Comment: arXiv admin note: text overlap with arXiv:2208.12887 |
| Databáze: | arXiv |
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