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

This is the second in a series of two papers in which the patch recovery technique proposed by Zienkiewicz and Zhu [1–3] is analyzed. In the first paper [4], we have shown that the recovered derivative by the least-squares fitting is superconvergent for the two-point boundary value problems. In the present work, we consider the two-dimensional case in which the tensor product elements are used. We show that the patch recovery technique yields superconvergence recovery for the gradient in both the L2-norm and the L∞-norm. Consequently, the error estimator based on the recovered gradient is asymptotically exact.