# American Institute of Mathematical Sciences

August  2005, 5(3): 769-798. doi: 10.3934/dcdsb.2005.5.769

## The polynomial-preserving recovery for higher order finite element methods in 2D and 3D

 1 College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China 2 Department of Mathematics, Wayne State University, Detroit, MI 48202, United States

Received  October 2004 Revised  February 2005 Published  May 2005

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.
Citation: A. Naga, Z. Zhang. The polynomial-preserving recovery for higher order finite element methods in 2D and 3D. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 769-798. doi: 10.3934/dcdsb.2005.5.769
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