An a-posteriori error estimator for linear elastic fracture mechanics using the stable generalized/extended finite element method

In this study, a recovery-based a-posteriori error estimator originally proposed for the Corrected XFEM is investigated in the framework of the stable generalized FEM (SGFEM). Both Heaviside and branch functions are adopted to enrich the approximations in the SGFEM. Some necessary adjustments to adapt the expressions defining the enhanced stresses in the original error estimator are discussed in the SGFEM framework. Relevant aspects such as effectivity indexes, error distribution, convergence rates and accuracy of the recovered stresses are used in order to highlight the main findings and the effectiveness of the error estimator. Two benchmark problems of the 2-D fracture mechanics are selected to assess the robustness of the error estimator hereby investigated. The main findings of this investigation are: the SGFEM shows higher accuracy than G/XFEM and a reduced sensitivity to blending element issues. The error estimator can accurately capture these features of both methods.