The polynomial-preserving recovery for higher order finite element methods

(Communicated by Jie Shen) Abstract. The Polynomial-Preserving Recovery (PPR) technique is extended to recover continuous gradients from C 0 finite element solutions of an arbitrary order in 2D and 3D problems. The stability of the PPR is theoretically investigated in a general framework. In 2D, the stability is established under a simple geometric condition. The numerical experiments demonstrated that the PPR-recovered gradient enjoys superconvergence, and the Zienkiewicz-Zhu error estimator based on the PPR-recovered gradient is asymptotically exact