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Some Weighted Averaging Methods for Gradient Recovery

Published online by Cambridge University Press:  03 June 2015

Yunqing Huang ,
Kai Jiang  and
Nianyu Yi
Yunqing Huang*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China
Kai Jiang*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China
Nianyu Yi*
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China
*
Corresponding author. URL: http://math.xtu.edu.cn/myphp/math/personal/huangyq/index.htm, Email: huangyq@xtu.edu.cn
Email: jkxtu@yahoo.com.cn
Email: yinianyu365109@126.com
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Abstract

We propose some new weighted averaging methods for gradient recovery, and present analytical and numerical investigation on the performance of these weighted averaging methods. It is shown analytically that the harmonic averaging yields a superconvergent gradient for any mesh in one-dimension and the rectangular mesh in two-dimension. Numerical results indicate that these new weighted averaging methods are better recovered gradient approaches than the simple averaging and geometry averaging methods under triangular mesh.

Keywords

65N1265N1565N3065D1074S0541A1041A25Finite element methodweighted averaginggradient recovery
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 2 , April 2012 , pp. 131 - 155
Copyright
Copyright © Global-Science Press 2012

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