scholarly journals A posteriori error estimators for stabilized finite element approximations of an optimal control problem

2018 ◽  
Vol 340 ◽  
pp. 147-177 ◽  
Author(s):  
Alejandro Allendes ◽  
Enrique Otárola ◽  
Richard Rankin
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error Estimators ◽  
A Posteriori Error ◽  
Stabilized Finite Element ◽  
Error Estimators ◽  
Finite Element Approximations ◽  
Posteriori Error Estimators

A POSTERIORI ERROR ESTIMATORS VIA BUBBLE FUNCTIONS

1996 ◽  
Vol 06 (01) ◽  
pp. 33-41 ◽  
Author(s):  
ALESSANDRO RUSSO
Keyword(s):  
Finite Element ◽  
Posteriori Error ◽  
Error Estimator ◽  
A Posteriori ◽  
A Posteriori Error Estimators ◽  
Element Space ◽  
A Posteriori Error ◽  
Error Estimators ◽  
Bubble Functions ◽  
Posteriori Error Estimators

In this paper we discuss a way to recover a classical residual-based error estimator for elliptic problems by using a finite element space enriched with bubble functions. The advection-dominated case is also discussed.

Assessment of two a posteriori error estimators for elasticity problems

2008 ◽  
Vol 35 (11) ◽  
pp. 1239-1250
Author(s):  
A. H. ElSheikh ◽  
S. E. Chidiac ◽  
S. Smith
Keyword(s):  
Finite Element ◽  
Error Estimation ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error Estimators ◽  
A Posteriori Error ◽  
Estimation Techniques ◽  
Error Estimators ◽  
Elasticity Problems ◽  
Posteriori Error Estimators

The main focus of this paper is on the evaluation of local a posteriori error estimation techniques for the finite element method (FEM). The standard error estimation techniques are presented for the coupled displacement fields appearing in elasticity problems. The two error estimators, the element residual method (ERM) and Zienkiewicz–Zhu (ZZ) patch recovery technique, are evaluated numerically and then used as drivers for a mesh adaptation process. The results demonstrate the advantages of employing a posteriori error estimators for obtaining finite element solutions with a pre-specified error tolerance. Of the two methods, the ERM is shown to produce adapted meshes that are similar to those adapted by the exact error. Furthermore, the ERM provides higher quality estimates of the error in the global energy norm when compared to the ZZ estimator.

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