Estimation of the Accuracy of Finite-Element Petrov–Galerkin Method in Integrating the One-Dimensional Stationary Convection-Diffusion-Reaction Equation

2015 ◽  
Vol 67 (7) ◽  
pp. 1062-1090 ◽  
Author(s):  
S. V. Sirik
Keyword(s):  
Finite Element ◽  
Galerkin Method ◽  
Diffusion Reaction ◽  
Stationary Convection ◽  
Reaction Equation ◽  
One Dimensional ◽  
Convection Diffusion ◽  
The One

A Finite-Element Singular-Perturbation Technique for Convection-Diffusion Problems—Part 1: The One-Dimensional Case

1981 ◽  
Vol 48 (2) ◽  
pp. 265-271 ◽  
Author(s):  
Rafael F. Diaz-Munio ◽  
L. Carter Wellford
Keyword(s):  
Finite Element ◽  
Singular Perturbation ◽  
Perturbation Technique ◽  
Diffusion Equations ◽  
Shape Functions ◽  
Singular Perturbation Technique ◽  
One Dimensional ◽  
Convection Diffusion ◽  
The One ◽  
Standard Galerkin Method

Approximation procedures for the solution of convection-diffusion equations, occurring in various physical problems, are considered. Several finite-element algorithms based on singular-perturbation methods are proposed for the solution of these equations. A method of variational matched asymptotic expansions is employed to develop shape functions which are particularly useful when convection effects dominate diffusion effects in these problems. When these shape functions are used, in conjunction with the standard Galerkin method, to solve convection-diffusion equations, increased solution accuracy is obtained. Numerical results for various one-dimensional problems are presented to establish the workability of the developed methods.

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