Analysis of the superconvergent patch recovery technique and a posteriori error estimator in the finite element method (I) Original Research Article

This is the first in a series of two papers in which the patch recovery technique proposed by Zienkiewicz and Zhu is analyzed. In this work it is proved that the recovered derivative by the least-squares fitting is superconvergent for the two-point boundary value problems. Further, the a posteriori error estimator based on the recovery technique is shown to be asymptotically exact. This confirms the computational results obtained in [1,2].