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A-Posteriori Error Estimates for Uniform p-Version Finite Element Methods in Square

Part of:Partial differential equations, boundary value problemsPartial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  09 January 2017

Jianwei Zhou,
Danping Yang and
Yujie Liu
Jianwei Zhou*
Affiliation:
Department of Mathematics, Linyi University, Shandong 276005, China
Danping Yang*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, China
Yujie Liu*
Affiliation:
School of Data and Computational Science, Sun Yat-sen University, Guangzhou, Guangdong 510275, China
*
*Corresponding author. Email:jwzhou@yahoo.com (J. Zhou), dpyang@math.ecnu.edu.cn (D. Yang), liuyujie5@mail.sysu.edu.cn (Y. Liu)
*Corresponding author. Email:jwzhou@yahoo.com (J. Zhou), dpyang@math.ecnu.edu.cn (D. Yang), liuyujie5@mail.sysu.edu.cn (Y. Liu)
*Corresponding author. Email:jwzhou@yahoo.com (J. Zhou), dpyang@math.ecnu.edu.cn (D. Yang), liuyujie5@mail.sysu.edu.cn (Y. Liu)

Abstract

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In this work, the a-posteriori error indicator with an explicit formula for p-version finite element methods in square is investigated, and its reliable and efficient properties are deduced. Especially, this a-posteriori error indicator is determined by the right hand itemof themodel. We reformulate this a-posteriori error indicator with finite coefficients, which can be easily calculated during applications.

Keywords

a-posteriori error indicatorLegendre polynomialp-version finite element method

MSC classification

Secondary:65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods65M15: Error bounds

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017, pp. 272 - 281
Copyright
Copyright © Global-Science Press 2017 

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