Volume 55, Number 6, November-December 2021
|Page(s)||2643 - 2678|
|Published online||11 November 2021|
Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem
Unité de recherche “Mathématiques et Modélisation”, CAR, Faculté des Sciences, Université Saint-Joseph de Beyrouth, BP 11-514 Riad El Solh Beyrouth 1107 2050, Liban
2 Laboratoire Jean Kuntzmann, UMR CNRS 5224, Université Grenoble-Alpes, 700 Avenue Centrale, 38401 Saint-Martin-d’Hères, France
* Corresponding author: email@example.com
Accepted: 4 October 2021
In this article, we consider the convection-diffusion-reaction problem coupled the Darcy-Forchheimer problem by a non-linear external force depending on the concentration. We establish existence of a solution by using a Galerkin method and we prove uniqueness. We introduce and analyse a numerical scheme based on the finite element method. An optimal a priori error estimate is then derived for each numerical scheme. Numerical investigation are performed to confirm the theoretical accuracy of the discretization.
Mathematics Subject Classification: 35K05 / 25B45 / 74S05
Key words: Darcy-Forchheimer problem / convection-diffusion-reaction equation / finite element method / a priori error estimates
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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