Superconvergent recovery based error estimators

In this paper use is made of the superconvergence property of the recovered derivatives of piecewise linear finite element solutions of Poisson problems to construct efficient and simple to use error estimators which have the desired property of being asymptotically exact on structured triangulations. These error estimators may be classified into two types; viz, the flux projection estimators and the estimators based on interpolation error bounds. A scheme for the adaptive error control based on the refined global local method of Mao and Sun (Int. J. Numer. Methods Eng. 32, 1991) is introduced and supported by means of a numerical experiment.