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
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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.
-  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, https://doi.org/10.1090/S0025-5718-1986-0842127-7
-  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
- K. J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1982.
- 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," Mafelap V (J. Whiteman, ed.), Academic Press, 1985, pp. 491-503. MR 811058 (87f:65125)
- F. Brezzi & M. Fortin, "Numerical approximation of Mindlin-Reissner plates," Math. Comp., v. 47, 1986, pp.151-158. MR 842127 (87g:73057)
- P. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. MR 0520174 (58:25001)
- P. Destuynder, Thèse d'état, Paris, 1980.
- R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1977. MR 769654 (86m:76003)
- O. C. Zienkiewicz, The Finite Element Method in Engineering Sciences, McGraw-Hill, London, 1978. MR 0315970 (47:4518)