A simple error estimator and adaptive procedure for practical engineerng analysis

TLDR

The study presents a new, computationally simple error estimator that can be readily implemented in existing finite element codes. The estimator is computed using a straightforward algorithm that integrates easily into finite element software. The estimator accurately predicts global energy norm and local errors, enabling efficient adaptive mesh refinement or redesign to achieve target accuracy with few trials, and has also been successfully applied to other measures such as stress accuracy.

Abstract

Abstract A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes. The estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials. When combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable. Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.