Local error estimators for finite element linear analysis (Q1818493)

The authors propose a theory for estimating local errors either on stresses or on displacements which can be easily implemented. Two approaches can be distinguished depending on computational effort. The first one uses only a direct finite element analysis, whereas the second approach, following the initial finite element analysis, allows to conduct a reanalysis on \(\overline E\) and its surroundings for the \(\Sigma\) problem. A set of tools can be developed for automatically handling this latter stage; thus the second approach seems to be very attractive for stress estimation. The work is currently in progress for both two- and three-dimensional problems. Numerical examples are given for local error estimators for stresses.