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arXiv · 2211.10325

Numerical discretization of a Darcy-Forchheimer problem coupled with a singular heat equation

Alejandro Allendes·Gilberto Campaña·Enrique Otarola
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Abstract

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.

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Alejandro Allendes, Gilberto Campaña, Enrique Otarola. 2022-11-18. Numerical discretization of a Darcy-Forchheimer problem coupled with a singular heat equation. https://arxiv.org/abs/2211.10325

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