Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Uniform interior error estimates for the Reissner-Mindlin plate model

Author: Lucia Gastaldi
Journal: Math. Comp. 61 (1993), 539-567
MSC: Primary 65P05; Secondary 65N30, 73K10, 73V05
MathSciNet review: 1185245
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Interior error estimates are derived for the solution of the Reissner-Mindlin plate model discretized by mixed-interpolated elements. Precisely, it is shown that the error in an interior domain can be estimated by the sum of two terms: the first has the best order of accuracy that is possible locally for the finite element spaces used, the second is a weak norm of the error on a slightly larger domain (this term measures the effects from outside of this domain). The analysis is based on some abstract properties enjoyed by the finite element spaces considered.

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

  • [1] D. N. Arnold and R. S. Falk, The boundary layer for the Reissner-Mindlin plate model, SIAM J. Math. Anal. 26 (1989), 1276-1290. MR 1025088 (91c:65068)
  • [2] -, Edge effects in the Reissner-Mindlin plate theory, Analytic and Computational Models of Shells, A.S.M.E., New York, 1989.
  • [3] K. J. Bathe, Finite element procedures in engineering analysis, Prentice-Hall, Englewood Cliffs, NJ, 1982.
  • [4] J. H. Bramble, J. A. Nitsche, and A. H. Schatz, Maximum-norm interior estimates for Ritz-Galerkin methods, Math. Comp. 29 (1975), 677-688. MR 0398120 (53:1975)
  • [5] F. Brezzi, On the existence, uniqueness and approximations of saddle point problems arising from Lagrangian multipliers, RAIRO Anal. Numér. 2 (1974), 129-151. MR 0365287 (51:1540)
  • [6] F. Brezzi, K. J. Bathe, and M. Fortin, Mixed-interpolated elements for Reissner-Mindlin plates, Internat. J. Numer. Methods Eng. 28 (1989), 1787-1801. MR 1008138 (90g:73090)
  • [7] F. Brezzi and M. Fortin, Numerical approximation of Mindlin-Reissner plates, Math. Comp. 47 (1986), 151-158. MR 842127 (87g:73057)
  • [8] -, Mixed and hybrid finite element methods, Springer-Verlag, New York, 1991. MR 1115205 (92d:65187)
  • [9] F. Brezzi, M. Fortin, and R. Stenberg, A complete error analysis of some Reissner-Mindlin plate bending elements, Math. Models Methods Appl. Sci. 1 (1991), 125-151. MR 1115287 (92e:73030)
  • [10] T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces, Math. Comp. 34 (1990), 441-463. MR 559195 (81h:65014)
  • [11] L. Gastaldi, Uniform interior error estimates for Reissner-Mindlin plate model, Pubbl. IAN/CNR, N. 802, Pavia, 1991.
  • [12] L. Gastaldi and R. H. Nochetto, Quasi-optimal pointwise error estimates for the Reissner-Mindlin plate, SIAM J. Numer. Anal. 28 (1991), 363-377. MR 1087509 (92c:65129)
  • [13] J. Necas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967.
  • [14] J. A. Nitsche and A. H. Schatz, Interior estimates for Ritz-Galerkin methods, Math. Comp. 28 (1974), 937-958. MR 0373325 (51:9525)
  • [15] R. Scholtz, Optimal $ {L^\infty }$-estimates for a mixed finite element method for second order elliptic and parabolic problems, Calcolo 20 (1983), 355-377. MR 761790 (86j:65164)
  • [16] L. R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp. 54 (1990), 483-493. MR 1011446 (90j:65021)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65P05, 65N30, 73K10, 73V05

Retrieve articles in all journals with MSC: 65P05, 65N30, 73K10, 73V05

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society