Adaptive finite element analysis of crack propagation in elastic fracture mechanics based on averaging techniques

A goal-oriented a posteriori error estimator is presented in this paper for the error obtained while approximately evaluating the J-integral in elastic fracture mechanics using the finite element method. The J-integral provides a criterion for crack propagation of a pre-existing crack. Its accurate evaluation is therefore of considerable importance in engineering applications to prevent failure of structures. This goal can be attained by adaptive finite element methods based on the well-established strategy of solving an auxiliary dual problem in order to control the error of a (non)linear functional, here the J-integral. In this paper, the adaptive strategy is based on a goal-oriented a posteriori error estimator that uses averaging techniques. The paper is concluded by a numerical example that illustrates our theoretical results.