scholarly journals On the nonlinear convection-diffusion-reaction problem in a thin domain with a weak boundary absorption

2018 ◽  
Vol 17 (2) ◽  
pp. 579-592 ◽  
Author(s):  
Igor Pažanin ◽  
◽  
Marcone C. Pereira ◽  
Keyword(s):  
Diffusion Reaction ◽  
Thin Domain ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Weak Boundary ◽  
Boundary Absorption ◽  
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.

scholarly journals Hermite Method of Approximate Particular Solutions for Solving Time-Dependent Convection-Diffusion-Reaction Problems

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 188
Author(s):  
Jen-Yi Chang ◽  
Ru-Yun Chen ◽  
Chia-Cheng Tsai
Keyword(s):  
Shape Parameter ◽  
Source Term ◽  
Time Dependent ◽  
Diffusion Reaction ◽  
System Matrix ◽  
Time Step ◽  
Convection Diffusion ◽  
Particular Solutions ◽  
Particular Solution ◽  
Reaction Problem

This article describes the development of the Hermite method of approximate particular solutions (MAPS) to solve time-dependent convection-diffusion-reaction problems. Using the Crank-Nicholson or the Adams-Moulton method, the time-dependent convection-diffusion-reaction problem is converted into time-independent convection-diffusion-reaction problems for consequent time steps. At each time step, the source term of the time-independent convection-diffusion-reaction problem is approximated by the multiquadric (MQ) particular solution of the biharmonic operator. This is inspired by the Hermite radial basis function collocation method (RBFCM) and traditional MAPS. Therefore, the resultant system matrix is symmetric. Comparisons are made for the solutions of the traditional/Hermite MAPS and RBFCM. The results demonstrate that the Hermite MAPS is the most accurate and stable one for the shape parameter. Finally, the proposed method is applied for solving a nonlinear time-dependent convection-diffusion-reaction problem.

Sign in / Sign up

Export Citation Format

Share Document