The polynomial-preserving recovery for higher order finite elementmethods in 2D and 3D

A. Naga; Z. Zhang

doi:10.3934/dcdsb.2005.5.769

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2005, Volume 5, Issue 3: 769-798. Doi: 10.3934/dcdsb.2005.5.769

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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
2.
Department of Mathematics, Wayne State University, Detroit, MI 48202

Received: September 30, 2004

Revised: January 31, 2005

Published: July 2005

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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.

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Mathematics Subject Classification: 65N30, 65N15, 65N12, 65D10,74S05, 41A10, 41A25.

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