On mixed finite element methods for the Reissner-Mindlin plate model

Durán, Ricardo; Liberman, Elsa

doi:10.1090/S0025-5718-1992-1106965-0

On mixed finite element methods for the Reissner-Mindlin plate model
HTML articles powered by AMS MathViewer

by Ricardo Durán and Elsa Liberman PDF

Math. Comp. 58 (1992), 561-573 Request permission

Abstract:

In this paper we analyze the convergence of mixed finite element approximations to the solution of the Reissner-Mindlin plate problem. We show that several known elements fall into our analysis, thus providing a unified approach. We also introduce a low-order triangular element which is optimal-order convergent uniformly in the plate thickness.

References

D. N. Arnold, F. Brezzi, and M. Fortin, A stable finite element for the Stokes equations, Calcolo 21 (1984), no. 4, 337–344 (1985). MR 799997, DOI 10.1007/BF02576171
Douglas N. Arnold and Richard S. Falk, A uniformly accurate finite element method for the Reissner-Mindlin plate, SIAM J. Numer. Anal. 26 (1989), no. 6, 1276–1290. MR 1025088, DOI 10.1137/0726074
Douglas N. Arnold and Richard S. Falk, The boundary layer for the Reissner-Mindlin plate model, SIAM J. Math. Anal. 21 (1990), no. 2, 281–312. MR 1038893, DOI 10.1137/0521016
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

A simplified analysis of two plate bending elements—the MITC4 and MITC9 elements

A four-node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation

21

Franco Brezzi, Klaus-Jürgen Bathe, and Michel Fortin, Mixed-interpolated elements for Reissner-Mindlin plates, Internat. J. Numer. Methods Engrg. 28 (1989), no. 8, 1787–1801. MR 1008138, DOI 10.1002/nme.1620280806
Franco Brezzi, Jim Douglas Jr., Michel Fortin, and L. Donatella Marini, Efficient rectangular mixed finite elements in two and three space variables, RAIRO Modél. Math. Anal. Numér. 21 (1987), no. 4, 581–604 (English, with French summary). MR 921828, DOI 10.1051/m2an/1987210405811
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

Hybrid and mixed finite element methods

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
M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 7 (1973), no. R-3, 33–75. MR 343661
Vivette Girault and Pierre-Arnaud Raviart, Finite element methods for Navier-Stokes equations, Springer Series in Computational Mathematics, vol. 5, Springer-Verlag, Berlin, 1986. Theory and algorithms. MR 851383, DOI 10.1007/978-3-642-61623-5
P.-A. Raviart and J. M. Thomas, A mixed finite element method for 2nd order elliptic problems, Mathematical aspects of finite element methods (Proc. Conf., Consiglio Naz. delle Ricerche (C.N.R.), Rome, 1975) Lecture Notes in Math., Vol. 606, Springer, Berlin, 1977, pp. 292–315. MR 0483555