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SUMMARYAn 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.

In the paper we develop a structured approach to the a posteriori estimation of the error in the approximation obtained via the finite element method. This aids the classification of existing estimators as well as allowing new estimators to be proposed for new situations. A class of abstract estimators for finite elements of order p > 1 in ~n, n = 2, 3 based on exploiting the superconvergence phenomenon are analyzed. Mathematics Subject Classification (I991): 65N30

Abstract. In this paper we introduce techniques that allow us to define a posteriori error estimators via well-known recovery techniques. These allow us to construct a posteriori error estimators for relatively general problems. Further, we introduce new adaptive procedures that make use of these estimators and, in particular, describe an h-p procedure that is simple to implement and that, as numerical experiments have shown, attains an accelerated rate of convergence expected from the h-p version.

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