A simple error estimator for extended finite elements

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