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Based on the concept of constitutive relation error along with residual of both origin and dual problems,a goal-oriented error estimation method with extended degrees of freedom is developed in this paper.It leads to high quality local error bounds in the problem of fracture mechanics simulation with extended finite element method (XFEM),which involves enrichments to solve a stress singularity in the crack.Since goal-oriented error estimation with enriched degrees of freedom gives us a chance to evaluate the XFEM simulation,the stress intensity factor calculated by two kinds of XFEM programs developed by ourselves and by commercial code ABAQUS are compared in this work.With a comparison of reliability to the stress intensity factor calculation,the accuracy of two programs in different cases is evaluated and the source of error is discussed.A two dimensional XFEM example is carried out to illustrate the computational procedures.