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A Type of Finite Element Gradient Recovery Method based on Vertex-Edge-Face Interpolation: The Recovery Technique and Superconvergence Property

Published online by Cambridge University Press:  28 May 2015

Qun Lin  and
Hehu Xie
Qun Lin*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Hehu Xie*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
Corresponding author. Email: linq@lsec.cc.ac.cn
Corresponding author. Email: hhxie@lsec.cc.ac.cn
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Abstract

In this paper, a new type of gradient recovery method based on vertex-edge-face interpolation is introduced and analyzed. This method gives a new way to recover gradient approximations and has the same simplicity, efficiency, and superconvergence properties as those of superconvergence patch recovery method and polynomial preserving recovery method. Here, we introduce the recovery technique and analyze its superconvergence properties. We also show a simple application in the a posteriori error estimates. Some numerical examples illustrate the effectiveness of this recovery method.

Keywords

65N3065N1265N1565D1074S05Finite element methodleast-squares fittingvertex-edge-face interpolationsuperconvergencea posteriori error estimate
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 3 , August 2011 , pp. 248 - 263
Copyright
Copyright © Global-Science Press 2011

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