Error estimation in quantities of interest for XFEM using recovery techniques

Error estimators that measure the error in a quantity of interest defined by the analyst, instead of the energy norm, have become increasingly popular as they provide an error indicator for goal oriented adaptivity procedures. We propose an a posteriori recovery-based error estimation technique which considers the stress intensity factor K typical of singular problems as the quantity of interest for the extended finite element method. The recovery procedure relies on the use of an enhanced superconvergent patch recovery technique to evaluate highly accurate recovered stress fields for the primal and dual problems, which are then used to obtain a sharp error estimate. The results indicate an accurate estimation of the error in K for benchmark problems with exact solution.