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2011 (Vol. 3, Issue: 3)
Article Information:

Numerical Studies for Singularly Perturbed Convection Reaction Diffusion Problems in Two Dimensions

N.H. Sweilam, M.M. Khader and F.M. Atlan
Corresponding Author:  Dr. Nasser Hassan Sweilam 

Key words:  A posteriori error estimates, AMS Subject Classification (2000), finite element method, mesh refinement, stationary convection reaction diffusion problem, variational iteration method,
Vol. 3 , (3): 97-106
Submitted Accepted Published
2011 May, 27 2011 August, 05 2011 September, 25
Abstract:

In this study, we study the numerical solutions of singularly perturbed convection-reaction-diffusion problem over a square. Two different approaches are used to study the problem namely: Finite Element Method (FEM) based on a posteriori error estimate, and Variational Iteration Method (VIM). In this study, we use the adaptive h-refinement based on the a posteriori error estimate. Numerical simulation for the solution of the proposed problem using FEM and VIM is given. From this simulation we can found that the finite element method gives the solution with excellent agreement compared with the exact solution. Also, it's found that VIM is invalid for some values of the perturbed parameter g, but FEM overcome on this shortcoming.
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  Cite this Reference:
N.H. Sweilam, M.M. Khader and F.M. Atlan, 2011. Numerical Studies for Singularly Perturbed Convection Reaction Diffusion Problems in Two Dimensions.  Research Journal of Mathematics and Statistics, 3(3): 97-106.
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ISSN (Online):  2040-7505
ISSN (Print):   2042-2024
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