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.

A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
V. Dhanya Varma ◽  
Suresh Kumar Nadupuri
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Fluidized Beds ◽  
A Priori ◽  
Coupled System ◽  
Diffusion Reaction ◽  
Strongly Coupled ◽  
Convection Diffusion ◽  
Finite Element Approximations ◽  
Reaction Equations

Abstract In this work, a priori error estimates for finite element approximations to the governing equations of heat and mass transfer in fluidized beds are derived. These equations are time dependent strongly coupled system of five semilinear convection-diffusion-reaction equations. The a priori error estimates for all the five variables are obtained for the error measured in L ∞(L 2) and L 2 ( E ) ${L}^{2}\left(\mathcal{E}\right)$ , E $\mathcal{E}$ is the energy norm.

The Numerical Analysis and Simulation of a Linearized Crank-Nicolson H1-GMFEM for Nonlinear Coupled BBM Equations

2014 ◽  
Vol 513-517 ◽  
pp. 1919-1926 ◽  
Author(s):  
Min Zhang ◽  
Zu Deng Yu ◽  
Yang Liu ◽  
Hong Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Scheme ◽  
Mixed Finite Element ◽  
A Priori ◽  
Numerical Test ◽  
Mixed Finite Element Method ◽  
Spatial Direction ◽  
Time Direction ◽  
Crank Nicolson

In this article, the numerical scheme of a linearized Crank-Nicolson (C-N) method based on H1-Galerkin mixed finite element method (H1-GMFEM) is studied and analyzed for nonlinear coupled BBM equations. In this method, the spatial direction is approximated by an H1-GMFEM and the time direction is discretized by a linearized Crank-Nicolson method. Some optimal a priori error results are derived for four important variables. For conforming the theoretical analysis, a numerical test is presented.

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