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Goal oriented error estimation and adaptive procedures are essential for theaccurate and efficient evaluation of numerical simulations that involve complexdomains. By locally improving the approximation quality we can solve expensiveproblems which could result intractable otherwise. Here, we present an errorestimation technique for enriched finite element approximations that is basedon an equilibrated recovery technique, which considers the stress intensityfactor as the quantity of interest. The locally equilibrated superconvergentpatch recovery is used to obtain enhanced stress fields for the primal and dualproblems defined to evaluate the error estimate.

Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method