Advertisement

Nonconforming Rectangular Morley Finite Elements

  • A. B. Andreev
  • M. R. Racheva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

Abstract

We analyze some approximation properties of modified rectangular Morley elements applied to fourth-order problems. Degrees of freedom of integrals type are used which yields superclose property. Further asymptotic error estimates for biharmonic solutions are derived. Some interesting and new numerical results concerning plate vibration problems are also presented.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ciarlet, P.G.: Basic error estimates for elliptic problems. In: Ciarlet, P.G., Lions, J.L. (eds.) Finite Element Methods (Part 1), Handbook of Numerical Analysis, vol. 2, pp. 21–343. Elsevier Science Publishers, North-Holland (1991)Google Scholar
  2. 2.
    Wang, L., Xie, X.: Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems. eprint arXiv:1101.1218 (arXiv1101.1218W) (2011)Google Scholar
  3. 3.
    Zhang, H., Wang, M.: The Mathematical Theory of Finite Elements. Science Press, Beijing (1991)Google Scholar
  4. 4.
    Nicaise, S.: A posteriori error estimations of some cell-centered finite volume methods. SIAM J. Numer. Anal. 43(04), 1481–1503 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Brenner, S., Scott, L.R.: The Mathematical Theory for Finite Element Methods. Springer-Verlag, New York (1994)CrossRefGoogle Scholar
  6. 6.
    Lascaux, P., Lesaint, P.: Some nonconforming finite elements for the plate bending problem. Rev. Française Automat. Informat. Recherche Operationnelle Sér. Rouge Anal. Numer. R-1, 9–53 (1975)Google Scholar
  7. 7.
    Rannacher, D.: Nonconforming finite element method for eigenvalue problems in linear plate theory. Numer. Math. 3, 23–42 (1979)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Racheva M.R.: Approximation from below of the exact eigenvalues by means of nonconforming FEMs. Mathematica Balkanica (2012) (to appear)Google Scholar
  9. 9.
    Yang, Y.D.: A posteriori error estimates in Adini finite element for eigenvalue problems. J. Comput. Math. 18, 413–418 (2000)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • A. B. Andreev
    • 1
  • M. R. Racheva
    • 2
  1. 1.Department of InformaticsTechnical University of GabrovoGabrovoBulgaria
  2. 2.Department of MathematicsTechnical University of GabrovoGabrovoBulgaria

Personalised recommendations