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The simplest conforming anisotropic rectangular and cubic mixed finite elements for elasticity

Author

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  • Chen, Shao-chun
  • Sun, Yan-ping
  • Zhao, Ji-kun

Abstract

In this paper, we construct two simplest conforming rectangular elements for the linear elasticity problem under the Hellinger–Reissner variational principle. One is a rectangular element in 2D with only 8 degrees of freedom for the stress and 2 degrees of freedom for the displacement. Another one is a cubic element in 3D with only 18 + 3 degrees of freedom. We prove that the two elements are stable and anisotropic convergent. Numerical test is presented to illustrate the element is stable and effective.

Suggested Citation

  • Chen, Shao-chun & Sun, Yan-ping & Zhao, Ji-kun, 2015. "The simplest conforming anisotropic rectangular and cubic mixed finite elements for elasticity," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 292-303.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:292-303
    DOI: 10.1016/j.amc.2015.04.117
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    Cited by:

    1. Sun, Yan-Ping & Chen, Shao-Chun & Yang, Yong-Qin, 2019. "The families of nonconforming mixed finite elements for linear elasticity on simplex grids," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 348-362.

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