Abstract: An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error bounds in three-dimensional fracture mechanics simulation which involves enrichments to solve the singularity in crack tip. This enriched goal-oriented error estimation gives a chance to evaluate this continuumbased shell extended finite element method simulation. With comparisons of reliability to the stress intensity factor calculation in stretching and bending, the accuracy of the continuum-based shell extended finite element method simulation is evaluated, and the reason of error is discussed.

Key words: generalized mixed implicit quasi-equilibrium problem, auxiliary variational inequality, predictor-corrector iterative algorithms, partially relaxed implicit strong monotonicity, goal-oriented error estimation, finite element analysis, fracture mechanics, continuum-based shell