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The Highest Superconvergence of the Tri-linear Element for Schr\(\ddot{\text {o}}\)dinger Operator with Singularity

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Abstract

In this paper, the eigenvalues for Schr\(\ddot{\text {o}}\)dinger operator with singularity are analyzed. A special piecewise uniform rectangular partition is constructed and it has been proven that, under this partition, the tri-linear rectangular finite element method has the highest possible superconvergence rate for eigenvalue.

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Authors and Affiliations

  1. Department of Mathematics, Wenzhou University, Wenzhou, 320035, Zhejiang, People‘s Republic of China

    Wenming He

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

    Zhimin Zhang & Ren Zhao

Authors
  1. Wenming He
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  2. Zhimin Zhang
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  3. Ren Zhao
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Corresponding author

Correspondence to Wenming He.

Additional information

The first author is supported in part by the National Natural Science Foundation of China (11171257) and the Zhejiang Provincial Natural Science Foundation of China under Grant (No. Y15A010040); and the second author is supported in part by the US National Science Foundation through grant DMS-0115530.

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He, W., Zhang, Z. & Zhao, R. The Highest Superconvergence of the Tri-linear Element for Schr\(\ddot{\text {o}}\)dinger Operator with Singularity. J Sci Comput 66, 1–18 (2016). https://doi.org/10.1007/s10915-015-0007-6

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  • DOI: https://doi.org/10.1007/s10915-015-0007-6

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