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A quadrilateral nonconforming finite element for linear elasticity problem

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Abstract

In this paper, a four-parameter quadrilateral nonconforming finite element with DSP (double set parameters) is presented. Then we discuss the quadrilateral nonconforming finite element approximation to the linear elastic equations with pure displacement boundary. The optimal convergence rate of the method is established in the broken \(H^1\) energy and \(L^2\)-norms, and in particular, the convergence is uniform with respect to the Lamé parameter \(\lambda\). Also the performance of the scheme does not deteriorate as the material becomes nearly incompressible. Lastly, a numerical test is carried out, which coincides with our theoretical analysis.

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Authors and Affiliations

  1. Institute of Computational Mathematics, Chinese Academy of Science, P.O. Box 2719, Beijing, 100080, People’s Republic of China

    Shipeng Mao

  2. Department of Mathematics, Zhengzhou University, 450052, Zhengzhou, People’s Republic of China

    Shaochun Chen

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  1. Shipeng Mao
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  2. Shaochun Chen
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Correspondence to Shipeng Mao.

Additional information

The research is supported by NSF of China (No. 10471133) and the project of Creative Engineering of Henan Province of China.

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Mao, S., Chen, S. A quadrilateral nonconforming finite element for linear elasticity problem. Adv Comput Math 28, 81–100 (2008). https://doi.org/10.1007/s10444-006-9017-0

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  • DOI: https://doi.org/10.1007/s10444-006-9017-0

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