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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Convergence properties and numerical approximation of the solution of the Mindlin plate bending problem
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by Roger Pierre PDF
Math. Comp. 51 (1988), 15-25 Request permission


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.
    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 10.1090/S0025-5718-1986-0842127-7
  • Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. 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
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 15-25
  • MSC: Primary 73K10; Secondary 65N30, 73K25
  • DOI:
  • MathSciNet review: 942141