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Superconvergence of three dimensional Morley elements on cuboid meshes for biharmonic equations

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Abstract

In the present paper, superconvergence of second order, after an appropriate postprocessing, is achieved for three dimensional first order cuboid Morley elements of biharmonic equations. The analysis is dependent on superconvergence of second order for the consistency error and a corrected canonical interpolation operator, which help to establish supercloseness of second order for the corrected canonical interpolation. Then the final superconvergence is derived by a standard postprocessing. For first order nonconforming finite element methods of three dimensional fourth order elliptic problems, it is the first time that full superconvergence of second order is obtained without an extra boundary condition imposed on exact solutions. It is also the first time that superconvergence is established for nonconforming finite element methods of three dimensional fourth order elliptic problems. Numerical results are presented to demonstrate the validity of the theoretical results.

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Authors and Affiliations

  1. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Jun Hu

  2. LESC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Zhongci Shi

  3. School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Xueqin Yang

Authors
  1. Jun Hu
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  2. Zhongci Shi
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  3. Xueqin Yang
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Corresponding author

Correspondence to Xueqin Yang.

Additional information

Communicated by: Martin Stynes

The first author was supported by the NSFC Projects 11271035, 91430213 and 11421101.

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Hu, J., Shi, Z. & Yang, X. Superconvergence of three dimensional Morley elements on cuboid meshes for biharmonic equations. Adv Comput Math 42, 1453–1471 (2016). https://doi.org/10.1007/s10444-016-9470-3

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  • DOI: https://doi.org/10.1007/s10444-016-9470-3

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