An improvement of the EDI method in linear elastic fracture mechanics by means of an a posteriori error estimator in G

In this paper, an error estimator that quantifies the effect of the finite element discretization error on the computation of the stress intensity factor in linear elastic fracture mechanics is presented. In order to obtain the proposed estimator, a shape design sensitivity analysis (SDSA) is applied to the fracture mechanics problem. Following this approach, one of the most efficient post-processing techniques for computing the strain energy release rate G, the well-known EDI method, may be interpreted as a continuum method of the SDSA. The proposed error estimator is based on the recovery of the gradient fields and its reliability has been checked by means of numerical problems, yielding very good estimations of the true error. The new estimator remarkably improves the results given by a previous error estimator, which is based on a discrete analytical approach of SDSA. As a consequence, the combination of the new error estimator and the result given by the EDI method provides a much more accurate estimation of G.