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Some numerical quadrature schemes of a non-conforming quadrilateral finite element

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An Erratum to this article was published on 29 April 2012

Abstract

Numerical quadrature schemes of a non-conforming finite element method for general second order elliptic problems in two dimensional (2-D) and three dimensional (3-D) space are discussed in this paper. We present and analyze some optimal numerical quadrature schemes. One of the schemes contains only three sampling points, which greatly improves the efficiency of numerical computations. The optimal error estimates are derived by using some traditional approaches and techniques. Lastly, some numerical results are provided to verify our theoretical analysis.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, 200092, China

    Xiao-fei Guan

  2. School of Information Engineering, China University of Geosciences (Beijing), Beijing, 100083, China

    Ming-xia Li

  3. Department of Mathematics, Zhengzhou University, Zhengzhou, 450052, China

    Shao-chun Chen

Authors
  1. Xiao-fei Guan
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  2. Ming-xia Li
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  3. Shao-chun Chen
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Corresponding author

Correspondence to Xiao-fei Guan.

Additional information

Supported by the National Natural Science Foundation of China (No. 50838004, 50908167). The second author’s work is supported by the Fundamental Research Funds for the Central Universities of China (No. 2011YYL078) and the National Natural Science Foundation of China (No. 11101386).

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Guan, Xf., Li, Mx. & Chen, Sc. Some numerical quadrature schemes of a non-conforming quadrilateral finite element. Acta Math. Appl. Sin. Engl. Ser. 28, 117–126 (2012). https://doi.org/10.1007/s10255-012-0127-9

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  • DOI: https://doi.org/10.1007/s10255-012-0127-9

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