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 ultraconvergence at element edge centers for the regular pattern.
Number in Series
Applied Mathematics | Mathematics | Numerical Analysis and Computation
AMS Subject Classification
65N30, 65N15, 65N12, 65D10, 74S05, 41A10, 41A25
Zhang, Zhiming and Naga, Ahmed, "A Meshless Gradient Recovery Method Part I: Superconvergence Property" (2002). Mathematics Research Reports. 3.