This work presents a goal-oriented error estimator specifically developed to quantify the error in the Stress Intensity Factor (SIF) for problems in Linear Elastic Fracture Mechanics. The estimator is formulated within the framework of the Generalized/eXtended Finite Element Method (G/XFEM), a widely used numerical technique for solving problems involving discontinuities and singularities. The analysis focuses on two-dimensional cases, with the SIF computed using the Interaction Integral — an energy-based method expressed as a domain integral.To estimate the error, a dual problem is constructed using the same discretization space as the primal problem. The estimated SIF error is then derived from the energy norm errors of both problems. For the energy norm estimation, the ZZ-BD recovery-based estimator is employed. This technique builds a recovered stress field using special enrichment functions and solves block-diagonal systems of equations, ensuring both computational efficiency and high accuracy.Numerical results for a mixed-mode fracture problem confirm the effectiveness of the proposed strategy, resulting in effectivity indices close to unity. Furthermore, the element-wise distribution of the estimated error closely reflects the characteristics of the Interaction Integral. All simulations were performed using INSANE, an open-source platform developed at the Department of Structural Engineering of the Federal University of Minas Gerais.
