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A New Stabilization Method for the Elasticity Problem

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Abstract

In this paper, we consider the elasticity problem based on the Hellinger–Reissner variational principle. We use the \(C^0\) continuous arbitrary degree polynomial mixed finite element spaces to approximate the stress and displacement, and develop a new stabilization method for the finite element space pairs to overcome the lack of the inf-sup condition, then we give the corresponding error estimates of the stabilization approximation scheme. At last, we implement a numerical example to test the stability and effectiveness of the proposed method.

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Acknowledgments

This work was supported by NSFC 10971203 and NSFC 11271340.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    Dong-yang Shi

  2. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Ming-hao Li

  3. Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang, 471023, China

    Chao Xu

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  1. Dong-yang Shi
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  2. Ming-hao Li
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  3. Chao Xu
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Correspondence to Ming-hao Li.

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Shi, Dy., Li, Mh. & Xu, C. A New Stabilization Method for the Elasticity Problem. J Sci Comput 65, 1025–1038 (2015). https://doi.org/10.1007/s10915-015-9996-4

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