Finite element approximation for a convective Brinkman--Forchheimer problem coupled with a heat equation
Numerical Analysis
2024-11-21 v2 Numerical Analysis
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.
Cite
@article{arxiv.2403.09872,
title = {Finite element approximation for a convective Brinkman--Forchheimer problem coupled with a heat equation},
author = {Gilberto Campaña and Pablo Muñoz and Enrique Otarola},
journal= {arXiv preprint arXiv:2403.09872},
year = {2024}
}