Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Convergence properties and numerical approximation of the solution of the Mindlin plate bending problem

Author: Roger Pierre
Journal: Math. Comp. 51 (1988), 15-25
MSC: Primary 73K10; Secondary 65N30, 73K25
MathSciNet review: 942141
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the behavior of the solution of the Mindlin problem when the thickness becomes small, paying particular attention to the shear stress. We also propose a modification of a known scheme that allows the use of linear finite element approximation and we prove optimal error bounds.

References [Enhancements On Off] (What's this?)

    K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1982.
  • 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, The mathematics of finite elements and applications, V (Uxbridge, 1984) Academic Press, London, 1985, pp. 491–503. MR 811058
  • F. Brezzi and M. Fortin, Numerical approximation of Mindlin-Reissner plates, Math. Comp. 47 (1986), no. 175, 151–158. MR 842127, DOI
  • Philippe G. Ciarlet, The finite element method for elliptic problems, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. Studies in Mathematics and its Applications, Vol. 4. MR 0520174
  • P. Destuynder, Thèse d’état, Paris, 1980.
  • Roger Temam, Navier-Stokes equations, 3rd ed., Studies in Mathematics and its Applications, vol. 2, North-Holland Publishing Co., Amsterdam, 1984. Theory and numerical analysis; With an appendix by F. Thomasset. MR 769654
  • O. C. Zienkiewicz, The finite element method in engineering science, McGraw-Hill, London-New York-Düsseldorf, 1971. The second, expanded and revised, edition of The finite element method in structural and continuum mechanics. MR 0315970

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 73K10, 65N30, 73K25

Retrieve articles in all journals with MSC: 73K10, 65N30, 73K25

Additional Information

Article copyright: © Copyright 1988 American Mathematical Society