| Issue |
ESAIM: M2AN
Volume 55, Number 6, November-December 2021
|
|
|---|---|---|
| Page(s) | 2643 - 2678 | |
| DOI | https://doi.org/10.1051/m2an/2021066 | |
| Published online | 11 November 2021 | |
Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem
1
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: faouzi.triki@univ-grenoble-alpes.fr
Received:
18
March
2021
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.