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

Goal oriented error estimation and adaptive procedures are essential for
the accurate and efficient evaluation of finite element numerical simulations
that involve complex domains. By locally improving the approximation qual-
ity, for example, by using the extended finite element method (XFEM), we
can solve expensive problems which could result intractable otherwise. Here,
we present an error estimation technique for enriched finite element approxi-
mations that is based on an equilibrated recovery technique, which considers
the stress intensity factor as the quantity of interest. The locally equilibrated
superconvergent patch recovery is used to obtain enhanced stress fields for the
primal and dual problems defined to evaluate the error estimate.