Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem

Toni Sayah (1) , Georges Semaan (1) , Faouzi Triki (2)

1 USJ - Université Saint-Joseph de Beyrouth
2 EDP - Equations aux Dérivées Partielles

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.

Mots clés: a priori error estimates; Darcy-Forchheimer problem; convection-diffusion-reaction equation; finite element method

Domaines: Analyse numérique [math.NA]; Mathématiques [math]

Toni Sayah, Georges Semaan, Faouzi Triki. Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (6), pp.2643 - 2678. ⟨10.1051/m2an/2021066⟩. ⟨hal-03175608⟩