Finite element superconvergence approximation for one-dimensional singularly perturbed problems

2002 ◽  
Vol 18 (3) ◽  
pp. 374-395 ◽  
Author(s):  
Zhimin Zhang
Keyword(s):  
Finite Element ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
One Dimensional

A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems

2017 ◽  
Vol 17 (2) ◽  
pp. 337-349 ◽  
Author(s):  
Christos Xenophontos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fourth Order ◽  
Hermite Polynomials ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
The Finite Element Method ◽  
Singularly Perturbed Problems ◽  
Exponentially Graded ◽  
Element Method

AbstractWe consider fourth order singularly perturbed problems in one-dimension and the approximation of their solution by the h version of the finite element method. In particular, we use piecewise Hermite polynomials of degree ${p\geq 3}$ defined on an exponentially graded mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at the optimal rate when the error is measured in both the energy norm and a stronger, ‘balanced’ norm. Finally, we illustrate our theoretical findings through numerical computations, including a comparison with another scheme from the literature.

A finite element method for two–parameter singularly perturbed problems in 2D

PAMM ◽  
2006 ◽  
Vol 6 (1) ◽  
pp. 771-772 ◽  
Author(s):  
Ljiljana Teofanov ◽  
Hans-Görg Roos ◽  
Helena Zarin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
Two Parameter ◽  
Element Method
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