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Local superconvergence of post-processed high-order finite volume element solutions

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Abstract

Local superconvergence properties of the post-processed finite volume element method (FVEM) are studied. Some interpolation/extrapolation post-processing techniques are applied to a class of k th-order (k ≥ 2) FVE solutions for elliptic equations. A local analysis tool for the finite volume method is developed to analyze the proposed method, and some superconvergence results are established. The theoretical findings are supported by several numerical experiments.

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Acknowledgments

The authors are grateful to Dr. Yanhui Zhou for his help in numerical experiments.

Funding

Q. Zou: Research supported in part by the special project High Performance Computing of National Key Research and Development Program 2016YFB0200604,and Guangdong Provincial NSF Grant 2017B030311001.W. He: Research supported in part by NSFC Grant 11671304 and 11771338. Z.Zhang: Research supported in part by NSFC Grants 11871092, 11926356, and NASF U1930402.

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Authors and Affiliations

  1. Department of Mathematics, Lingnan Normal University, Zhanjiang, 524048, Guangdong, China

    Wenming He

  2. Beijing Computational Science Research Center, Beijing, 100193, China

    Zhimin Zhang

  3. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Zhimin Zhang

  4. School of Data and Computer Science, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, 510006, China

    Qingsong Zou

Authors
  1. Wenming He
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  2. Zhimin Zhang
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  3. Qingsong Zou
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Correspondence to Qingsong Zou.

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Communicated by: Long Chen

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He, W., Zhang, Z. & Zou, Q. Local superconvergence of post-processed high-order finite volume element solutions. Adv Comput Math 46, 60 (2020). https://doi.org/10.1007/s10444-020-09801-2

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