Free Access
Issue
ESAIM: M2AN
Volume 38, Number 6, November-December 2004
Page(s) 1055 - 1070
DOI https://doi.org/10.1051/m2an:2004050
Published online 15 December 2004
  1. S.M. Alessandrini, D.N. Arnold, R.S. Falk and A.L. Madureira, Derivation and justification of plate models by variational methods, in Plates and Shells, M. Fortin Ed., AMS, Providence, CRM Proc. Lect. Notes Ser. 21 (1999) 1–20. [Google Scholar]
  2. D.N. Arnold and R.S. Falk, A uniformly accurate finite element method for the Reissner-Mindlin plate. SIAM J. Numer. Anal. 26 (1989) 1276–1290. [CrossRef] [MathSciNet] [Google Scholar]
  3. K.J. Bathe and F. Brezzi, On the convergence of a four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation in Mathematics of Finite Elements an Applications V, J.R. Whiteman Ed., Academic Press, London (1985) 491–503. [Google Scholar]
  4. K.J. Bathe and E.N. Dvorkin, A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. Int. J. Numer. Methods Eng. 21 (1985) 367–383. [Google Scholar]
  5. A. Bermúdez and R. Rodríguez, Finite element computation of the vibration modes of a fluid-solid system. Comp. Methods Appl. Mech. Eng. 119 (1994) 355–370. [CrossRef] [Google Scholar]
  6. A. Bermúdez, P. Gamallo and R. Rodríguez, An hexahedral face element for elastoacoustic vibration problems. J. Comp. Acoust. 119 (1994) 355–370. [Google Scholar]
  7. A. Bermúdez, R. Durán, M.A. Muschietti, R. Rodríguez and J. Solomin, Finite element vibration analysis of fluid-solid systems without spurious modes. SIAM J. Numer. Anal. 32 (1995) 1280–1295. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York (1991). [Google Scholar]
  9. F. Brezzi, M. Fortin and R. Stenberg, Quasi-optimal error bounds for approximation of shear-stresses in Mindlin-Reissner plate models. Math. Models Methods Appl. Sci. 1 (1991) 125–151. [CrossRef] [MathSciNet] [Google Scholar]
  10. R. Durán and E. Liberman, On mixed finite element methods for the Reissner-Mindlin plate model. Math. Comp. 58 (1992) 561–573. [CrossRef] [MathSciNet] [Google Scholar]
  11. R. Durán, L. Hervella-Nieto, E. Liberman, R. Rodríguez and J. Solomin, Approximation of the vibration modes of a plate by Reissner-Mindlin equations. Math. Comp. 68 (1999) 1447–1463. [CrossRef] [MathSciNet] [Google Scholar]
  12. R. Durán, L. Hervella-Nieto, E. Liberman, R. Rodríguez and J. Solomin, Finite element analysis of the vibration problem of a plate coupled with a fluid. Numer. Math. 86 (2000) 591–616. [CrossRef] [MathSciNet] [Google Scholar]
  13. R. Durán, E. Hernández, L. Hervella-Nieto, E. Liberman and R. Rodríguez, Computation of the vibration modes of plates and shells by low-order MITC quadrilateral finite elements. SIAM J. Numer. Anal. 41 (2003) 1751–1772. [CrossRef] [MathSciNet] [Google Scholar]
  14. P. Gamallo, Métodos numéricos de elementos finitos en problemas de interacción fluido-estructura. Ph.D. Thesis, U. de Santiago de Compostela, Spain (2002). [Google Scholar]
  15. V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo (1986). [Google Scholar]
  16. T.J.R. Hughes, The Finite Element Method: Linear Static and Dinamic Finite Element Analysis. Prentice-Hall, Englewood Cliffs, NJ (1987). [Google Scholar]
  17. H.J.-P. Morand and R. Ohayon, Fluid-structure interactions. John Wiley & Sons, New York (1995). [Google Scholar]
  18. R. Rodríguez and J. Solomin, The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems. Math. Comp. 65 (1996) 1463–1475. [CrossRef] [MathSciNet] [Google Scholar]
  19. P.A. Raviart and J.M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of Finite Element Methods, Springer-Verlag, Berlin, Heidelberg, New York. Lect. Notes Math. 606 (1977) 292–315. [CrossRef] [Google Scholar]
  20. R. Stenberg and M. Suri, An hp error analysis of MITC plate elements. SIAM J. Numer. Anal. 34 (1997) 544–568. [CrossRef] [MathSciNet] [Google Scholar]
  21. J.M. Thomas, Sur l'analyse numérique des méthodes d'éléments finis hybrides et mixtes. Thèse de Doctorat d'Etat, Université Pierre et Marie Curie, Paris 6, France (1977). [Google Scholar]

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