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The Highest Superconvergence Analysis of ADG Method for Two Point Boundary Values Problem

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Abstract

In this paper, an averaging discontinuous Galerkin (ADG) method for two point boundary value problems is analyzed. We prove, for any even polynomial degree k, the numerical flux convergence at a rate of \(2k+2\) for all mesh nodes (in particular, the numerical flux for \(k=0\) has the second order superconvergence rate). Numerical experiments are shown to demonstrate the theoretical results.

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Acknowledgments

The authors would like to thank the anonymous referees for the valuable comments and constructive suggestions to improve this paper.

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Authors and Affiliations

  1. Key Laboratory of High Performance Computing and Stochastic Information Processing ( Ministry of Education of China ), College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Jiangxing Wang, Chuanmiao Chen & Ziqing Xie

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  1. Jiangxing Wang
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  2. Chuanmiao Chen
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  3. Ziqing Xie
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Correspondence to Chuanmiao Chen.

Additional information

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11171104, 91430107) and the Construct Program of the Key Discipline in Hunan.

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Wang, J., Chen, C. & Xie, Z. The Highest Superconvergence Analysis of ADG Method for Two Point Boundary Values Problem. J Sci Comput 70, 175–191 (2017). https://doi.org/10.1007/s10915-016-0247-0

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  • DOI: https://doi.org/10.1007/s10915-016-0247-0

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