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arXiv · 2403.09872

Finite element approximation for a convective Brinkman--Forchheimer problem coupled with a heat equation

Gilberto Campaña·Pablo Muñoz·Enrique Otarola
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Abstract

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.

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Gilberto Campaña, Pablo Muñoz, Enrique Otarola. 2024-03-14. Finite element approximation for a convective Brinkman--Forchheimer problem coupled with a heat equation. https://arxiv.org/abs/2403.09872

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