Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter

2019 ◽  
Vol 354 ◽  
pp. 533-544 ◽  
Author(s):  
Pratibhamoy Das ◽  
Jesus Vigo-Aguiar
Keyword(s):  
Small Perturbation ◽  
Numerical Approximation ◽  
Reaction Diffusion ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Optimal Order ◽  
Singularly Perturbed System ◽  
Perturbed System ◽  
Diffusion Problems

Finite Element Analysis of an Exponentially Graded Mesh for Singularly Perturbed Problems

2015 ◽  
Vol 15 (2) ◽  
pp. 135-143 ◽  
Author(s):  
Philippos Constantinou ◽  
Christos Xenophontos
Keyword(s):  
Finite Element ◽  
Reaction Diffusion ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Optimal Order ◽  
Singularly Perturbed Problems ◽  
Element Analysis ◽  
Convection Diffusion Equation ◽  
Natural Energy ◽  
Exponentially Graded

AbstractWe present the mathematical analysis for the convergence of an h version Finite Element Method (FEM) with piecewise polynomials of degree p ≥ 1, defined on an exponentially graded mesh. The analysis is presented for a singularly perturbed reaction-diffusion and a convection-diffusion equation in one dimension. We prove convergence of optimal order and independent of the singular perturbation parameter, when the error is measured in the natural energy norm associated with each problem. Numerical results comparing the exponential mesh with the Bakhvalov–Shishkin mesh from the literature are also presented.

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