A New Finite Element Gradient Recovery Method: Superconvergence Property

This is the first in a series of papers where a new gradient recovery method is introduced and analyzed. It is proved that the method is superconvergent for translation invariant finite element spaces of any order. The method maintains the simplicity, efficiency, and superconvergence properties of the Zienkiewicz-Zhu patch recovery method. In addition, under uniform triangular meshes, the method is superconvergent for the Chevron pattern, and ultraconvergent at element edge centers for the regular pattern. Applications of this new gradient recovery technique will be discussed in forthcoming papers.