A simple error estimator for extended finite elements

Abstract This short communication presents the idea of an a posteriori error estimate for enriched (extended) finite elements (XFEM). The enhanced strain field against which the XFEM strains are compared, is computed through extended moving least‐squares smoothing constructed using the diffraction method to preserve the discontinuity. The error estimator is the L 2 norm of the difference of the XFEM strain with the enhanced strain. We prove the concept of the proposed method on a 1D example with a singular solution and a 2D fracture mechanics example and conclude with some future work based on our paradigm. Copyright © 2007 John Wiley & Sons, Ltd.