An adaptive accuracy-based a posteriori error estimator (Q1205254)

A von Mises stress based finite element error estimator with a new concept of adaptive accuracy and mesh optimality is presented. The \(h\)- based adaptivity algorithm is based on a modified Zienkiewicz and Zhu a posteriori finite element error estimator [\textit{O. C. Zienkiewicz} and \textit{J. Z. Zhu}, Int. J. Numer. Methods Eng. 24, 337-357 (1987; Zbl 0602.73063)]. Contrary to the mathematical view that an optimal mesh is one in which the error in the solution as measured by element norms is uniform over the entire model, it is proposed that the accuracy requirement should be adapted according to the behaviour of the relative stress field distribution across the domain. In this approach a greater accuracy is required at highly stressed regions of the domain, while less accurate solutions are permitted at understressed regions.