Advertisement

VEM for the Reissner-Mindlin Plate Based on the MITC Approach: The Element of Degree 2

  • Claudia Chinosi
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

We consider the family of Virtual Elements introduced in Chinosi (Numer Methods Partial Differ Equ 34(4):1117–1144, 2018) for the Reissner-Mindlin plate problem. The family is based on the MITC approach of the FEM context. We analyze the element of degree 2 and compare it with the corresponding finite element MITC9. Moreover we propose a new approximation of the load in order to achieve the proper order of convergence in L2.

Notes

Acknowledgements

This research has a financial support of the Università del Piemonte Orientale.

References

  1. 1.
    L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L.D. Marini, A. Russo, Basic principles of virtual element methods. Math. Models Methods. Appl. Sci. 23(1), 199–214 (2013)MathSciNetCrossRefGoogle Scholar
  2. 2.
    L. Beirão da Veiga, F. Brezzi, L.D. Marini, Virtual elements for linear elasticity problems. SIAM J. Numer. Anal. 51(2), 794–812 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    L. Beirão da Veiga, F. Brezzi, L.D. Marini, A. Russo, Virtual element methods for general second order elliptic problems on polygonal meshes. Math. Models Methods Appl. Sci. 26(4), 729–750 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    F. Brezzi, K.J. Bathe, M. Fortin, Mixed-interpolated elements for Reissner-Mindlin plates. Int. J. Numer. Methods Eng. 28, 1787–1801 (1989)MathSciNetCrossRefGoogle Scholar
  5. 5.
    S. Cafiero, Virtual elements for the Reissner-Mindlin plates. Master’s degree thesis (Advisor: Beirão da Veiga L.), Università di Milano Bicocca, 2015Google Scholar
  6. 6.
    C. Chinosi, Virtual elements for the Reissner-Mindlin plate problem. Numer. Methods Partial Differ. Equ. 34(4), 1117–1144 (2018) https://doi.org/10.1002/num.22248MathSciNetCrossRefGoogle Scholar
  7. 7.
    P.A. Raviart, J.M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of the Finite Element Method. Lecture Notes in Mathematics, vol. 606 (Springer, Berlin, 1977), pp. 292–315Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Università del Piemonte OrientaleDipartimento di Scienze e Innovazione Tecnologica (DISIT)AlessandriaItaly

Personalised recommendations