American Institute of Mathematical Sciences

Advanced
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

A. Naga 1, and  Z. Zhang 2,

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.
Keywords: superconvergence, a posteriori error estimator., SPR, discrete least-squares fitting, finite element method, PPR.
Mathematics Subject Classification: 65N30, 65N15, 65N12, 65D10,74S05, 41A10, 41A2.
Citation: A. Naga, Z. Zhang. The polynomial-preserving recovery for higher order finite element methods in 2D and 3D. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 769-798. doi: 10.3934/dcdsb.2005.5.769
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