Mixed hp finite element method for singularly perturbed fourth order boundary value problems with two small parameters

2021 ◽  
Author(s):  
Christos Xenophontos ◽  
Sebastian Franz ◽  
Irene Sykopetritou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Small Parameters ◽  
Element Method ◽  
Hp Finite Element

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.

The Weighted Error Estimation of Finite Element Method for Two-Point Boundary Value Problem

2012 ◽  
Vol 182-183 ◽  
pp. 1571-1574
Author(s):  
Qi Sheng Wang ◽  
Jia Dao Lai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Error Estimation ◽  
Boundary Value ◽  
Point Boundary ◽  
Weighted Error ◽  
Element Method

In this paper, the weighed error estimation of finite element method for the two-point boundary value problems are discussed. Respectively, the norm estimation of the H1 and L2 are obtained.

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