Finite element approximation for a convective Brinkman--Forchheimer problem coupled with a heat equation
<|reference_start|>Finite element approximation for a convective Brinkman--Forchheimer problem coupled with a heat equation: We investigate a convective Brinkman--Forchheimer problem coupled with a heat transfer 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 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.<|reference_end|>
@article{campaña2024finite,
    title={Finite element approximation for a convective Brinkman--Forchheimer
  problem coupled with a heat equation},
    author={Gilberto Campa~na, Pablo Mu~noz, Enrique Otarola},
    journal={arXiv preprint arXiv:2403.09872},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.09872},
    primaryClass={math.NA cs.NA}
}