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Volume Locking Phenomena Arising in a Hybrid Symmetric Interior Penalty Method with Continuous Numerical Traces

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Domain Decomposition Methods in Science and Engineering XXIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 116))

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Abstract

A hybrid version of the symmetric interior penalty (HSIP) method is considered for linear elasticity problems for nearly incompressible materials. When the P 1 conforming finite element method is applied to such problems, volume locking phenomena occur. Discontinuous Galerkin (DG) methods are known as a remedy for the locking. The HSIP method has two unknowns which are approximations for the displacement and its trace on the skeleton. The latter is often called the numerical trace. The HSIP method with the discontinuous numerical trace is free from locking. On the other hand, it is numerically observed that the HSIP method with the continuous numerical trace causes volume locking phenomena when the P 1 elements are employed for the two unknowns. The numerical fact is mathematically proved in this paper.

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References

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Author information

Authors and Affiliations

  1. The University of Electro-Communications, Chofugaoka 1-5-1, Chofu, Tokyo, Japan

    Daisuke Koyama

  2. The University of Tokyo, Komaba 3-8-1, Meguro, Tokyo, Japan

    Fumio Kikuchi

Authors
  1. Daisuke Koyama
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  2. Fumio Kikuchi
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Corresponding author

Correspondence to Daisuke Koyama .

Editor information

Editors and Affiliations

  1. Dept. of Mathematical Sciences, KAIST, Daejeon, Korea (Republic of)

    Chang-Ock Lee

  2. Dept. of Computer Science, University of Colorado, Boulder, Colorado, USA

    Xiao-Chuan Cai

  3. Applied Math & Computational Science, KAUST, Thuwal, Saudi Arabia

    David E. Keyes

  4. Dept. of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. Mathematisches Institut, Universität zu Köln, Köln, Germany

    Axel Klawonn

  6. Dept. of Computational Science & Engineering, Yonsei University, Seoul, Korea (Republic of)

    Eun-Jae Park

  7. Courant Institute of Mathematical Sciences, New York University, New York, New York, USA

    Olof B. Widlund

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Koyama, D., Kikuchi, F. (2017). Volume Locking Phenomena Arising in a Hybrid Symmetric Interior Penalty Method with Continuous Numerical Traces. In: Lee, CO., et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_37

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