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Two robust nonconforming \(\hbox {H}^2\)-elements for linear strain gradient elasticity

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Abstract

We propose two finite elements to approximate a boundary value problem arising from strain gradient elasticity, which is a high order perturbation of the linearized elastic system. Our elements are \(\hbox {H}^2\)-nonconforming while \(\hbox {H}^1\)-conforming. We show both elements converge in the energy norm uniformly with respect to the perturbation parameter.

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Acknowledgements

The work of Li was supported by Science Challenge Project No. TZ 2016003. The work of Ming was partially supported by the National Natural Science Foundation of China for Distinguished Young Scholars 11425106, and National Natural Science Foundation of China Grants 91630313, and by the support of CAS NCMIS. The work of Shi was partially supported by the National Natural Science Foundation of China Grant 11371359. We are grateful to the anonymous referees for their valuable suggestions.

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Authors and Affiliations

  1. Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang, 621900, China

    Hongliang Li

  2. The State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55, Zhong-Guan-Cun East Road, Beijing, 100190, China

    Pingbing Ming & Zhong-ci Shi

  3. University of Chinese Academy of Sciences, Beijing, 100049, China

    Pingbing Ming & Zhong-ci Shi

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  1. Hongliang Li
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  3. Zhong-ci Shi
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Correspondence to Pingbing Ming.

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Li, H., Ming, P. & Shi, Zc. Two robust nonconforming \(\hbox {H}^2\)-elements for linear strain gradient elasticity. Numer. Math. 137, 691–711 (2017). https://doi.org/10.1007/s00211-017-0890-x

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  • DOI: https://doi.org/10.1007/s00211-017-0890-x

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