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Superconvergence and Asymptotic Expansions for Bilinear Finite Volume Element Approximations

Published online by Cambridge University Press:  28 May 2015

Cunyun Nie ,
Shi Shu ,
Haiyuan Yu  and
Juan Wu
Cunyun Nie*
Affiliation:
Department of Mathematics and Physics, Hunan Institute of Engineering, Hunan 411104, China
Shi Shu*
Affiliation:
Hunan Key Laboratory for Computation & Simulation in Science and Engineering and Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, Xiangtan University, Hunan 411105, China
Haiyuan Yu*
Affiliation:
Hunan Key Laboratory for Computation & Simulation in Science and Engineering and Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, Xiangtan University, Hunan 411105, China
Juan Wu*
Affiliation:
Hunan Key Laboratory for Computation & Simulation in Science and Engineering and Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, Xiangtan University, Hunan 411105, China
*
Corresponding author.Email address:ncyl028@gmail.com
Corresponding author.Email address:shushi@xtu.edu.cn
Corresponding author.Email address:yuhaiyuan2118@sina.com
Corresponding author.Email address:12819023@qq.com
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Abstract

Aiming at the isoparametric bilinear finite volume element scheme, we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids. Furthermore, we prove that the approximate derivatives are convergent of order two. Finally, numerical examples verify the theoretical results.

Keywords

65M1065M0841A60Isoparametric bilinear finite volume element schemeasymptotic expansionhigh accuracy combination formulasuperconvergence
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 2 , May 2013 , pp. 408 - 423
Copyright
Copyright © Global Science Press Limited 2013

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