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

2024/03/14 by Campaña, Gilberto, Muñoz, Pablo, Otarola, Enrique
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2403.09872

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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