scholarly journals Preserving nonnegativity of an affine finite element approximation for a convection–diffusion–reaction problem

2016 ◽  
Vol 306 ◽  
pp. 286-299 ◽  
Author(s):  
Javier Ruiz-Ramírez
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Diffusion Reaction ◽  
Element Approximation ◽  
Convection Diffusion ◽  
Reaction Problem

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

2021 ◽  
Author(s):  
Toni Sayah ◽  
Georges Semaan ◽  
Faouzi Triki
Keyword(s):  
Finite Element ◽  
Numerical Scheme ◽  
A Priori ◽  
Diffusion Reaction ◽  
The Finite Element Method ◽  
Existence Of A Solution ◽  
A Priori Error Estimate ◽  
Convection Diffusion ◽  
Reaction Problem ◽  
Theoretical Accuracy

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.

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