A model study of the quality of a posteriori error estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles

1994 ◽  
Vol 114 (3-4) ◽  
pp. 307-378 ◽  
Author(s):  
I Babuška ◽  
T Strouboulis ◽  
C.S Upadhyay
Keyword(s):  
Error Estimation ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error Estimators ◽  
A Posteriori Error ◽  
Error Estimators ◽  
Model Study ◽  
Uniform Grids ◽  
Posteriori Error Estimators

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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