Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates

P. Peisker; D. Braess

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1992)

  • Volume: 26, Issue: 5, page 557-574
  • ISSN: 0764-583X

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Peisker, P., and Braess, D.. "Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 26.5 (1992): 557-574. <http://eudml.org/doc/193676>.

@article{Peisker1992,
author = {Peisker, P., Braess, D.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {thickness parameter; Helmholtz decomposition},
language = {eng},
number = {5},
pages = {557-574},
publisher = {Dunod},
title = {Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates},
url = {http://eudml.org/doc/193676},
volume = {26},
year = {1992},
}

TY - JOUR
AU - Peisker, P.
AU - Braess, D.
TI - Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1992
PB - Dunod
VL - 26
IS - 5
SP - 557
EP - 574
LA - eng
KW - thickness parameter; Helmholtz decomposition
UR - http://eudml.org/doc/193676
ER -

References

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  1. [1] D. N. ARNOLD & R. S. FALK, A uniformly accurate finite element method for the Mindlin-Reissner plate, SIAM J. Numer. Anal. 26, 1276-1290 (1989). Zbl0696.73040MR1025088
  2. [2] K. J. BATHE & F. BREZZI, On the convergence of a four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. In Proceeding Conf. on Mathematics of Finite Elements and Applications 5 (J. R. Whiteman, ed.), Academic Press 1985, pp. 491-503. Zbl0589.73068MR811058
  3. [3] K. J. BATHE, F. BREZZI & S. W. CHO, The MITC7 and MITC9 plate bending elements, J. Computers & Structures 32, 797-814 (1989). Zbl0705.73241
  4. [4] K. J. BATHE & E. N. DVORKIN, A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation, Int. J. Num. Meth. Eng. 21, 367-383 (1985). Zbl0551.73072
  5. [5] F. BREZZI, K. J. BATHE & M. FORTIN, Mixed-interpolated elements for Reissner-Mindlin plates, Int J. Num. Meth. Eng. 28, 1787-1801 (1989). Zbl0705.73238MR1008138
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  9. [9] F. BREZZI & J. PITKÄRANTA, On the stabilization of finite element approximations of the Stokes equations. In « Efficient Solutions of Elliptic Systems » (W. Hackbusch, ed.), Vieweg, Braunschweig 1984, 11-19. Zbl0552.76002MR804083
  10. [10] P. G. CIARLET, The Finite Element Method for Elliptic Problems. North Holland 1978. Zbl0383.65058MR520174
  11. [11] J. Jr. DOUGLAS & J. E. ROBERTS, Global estimates for mixed methods for second order elliptic equations, Math. Comp. 44, 39-52 (1985). Zbl0624.65109MR771029
  12. [12] L. P. FRANCA & R. STENBERG, A modification of a low order Reissner-Mindlin plate bending element. Rapport de Recherche No 1084 INRIA-Rocquencourt, France, 1989. 
  13. [13] V. GIRAULT & P. A. RAVIART, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, Berlin, 1986. Zbl0585.65077MR851383
  14. [14] Z. HUANG, A multi-grid algorithm for mixed problems with penalty, Math. 57, 227-247 (1990). Zbl0712.73106MR1057122
  15. [15] P. A. RAVIART & J. M. THOMAS, A mixed finite element method for second order elliptic problems In « Mathematical Aspects of Finite Element Methods » (I. Galligani and E. Magenes, eds.), pp 292-315, Springer Verlag 1977. Zbl0362.65089MR483555
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  17. [17] F. BREZZI & M. FORTIN, Mixed and Hybrid Finite Elements, Springer Verlag 1991. Zbl0788.73002MR1115205

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