On adaptive strategies and error control in fracture mechanics

摘要

Finite element approximations in elastic fracture mechanics are traditionally carried out on a priori constructed meshes with singularity elements that surrounds the crack tip. In this contribution we discuss an adaptive algorithm based on goal oriented error measures using ordinary elements and a p-refinement for the linearization of the secant forms. The numerical experiments show that good results can be obtained without imposition of hands before the computations starts. Furthermore, we note that it is often possible, for engineering goal quantities, to linearize the data to the dual problem such that additional discretization error is avoided, and the error representation formula is in a sense trivial.