Enhanced recovery techniques for accurate evaluation of error estimates in FE aproximations

When modelling critical structures, it is crucial to rationally assess the outcome of numerical simu- lations. Specifically, error estimation strategies are key tools in critical decision-based processes. The development of design tools that enhance performance of the final product and give reliability on the calculations is essential in todays industrial environment, which increasingly seeks to reduce develop- ment times for new products while improving the quality. During the last years there has been an increasing interest on the use of error estimates which help to measure and control the error committed in standard or enriched finite element approximations. The error can be defined in terms of energy norm or in quantities relevant for design purposes (such as the mean stress value in a particular area, displacements, the stress intensity factor for fracture problems). In this work, we discuss the use of different a posteriori recovery techniques to evaluate error estimates for different finite element (FE) approximations. These techniques are based on equilibrated supercon- vergent patch recovery or equilibrated moving least squares procedures and can be used in smooth or singular problems. Numerical results show the capabilities of the proposed techniques to provide good error estimates.