Analysis of the Zienkiewicz–Zhu a‐posteriori error estimator in the finite element method

Abstract An a‐posteriori error estimator for finite element analysis proposed by Zienkiewicz and Zhu is analysed and shown to be effective and convergent. In addition we analyse wider classes of estimators of which the Zienkiewicz–Zhu estimator is a special case. It is shown that some of these estimators will be asymptotically exact. Numerical evidence is presented supporting the analysis.