Uniform interior error estimates for the Reissner-Mindlin plate model. (English) Zbl 0784.73046

Summary: 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.


74K20 Plates
74S05 Finite element methods applied to problems in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
Full Text: DOI


[1] 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. · Zbl 0696.73040 · doi:10.1137/0726074
[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] James H. Bramble, Joachim A. Nitsche, and Alfred H. Schatz, Maximum-norm interior estimates for Ritz-Galerkin methods, Math. Comput. 29 (1975), 677 – 688. · Zbl 0316.65023
[5] F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 8 (1974), no. R-2, 129 – 151 (English, with loose French summary). · Zbl 0338.90047
[6] 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. · Zbl 0705.73238 · doi:10.1002/nme.1620280806
[7] F. Brezzi and M. Fortin, Numerical approximation of Mindlin-Reissner plates, Math. Comp. 47 (1986), no. 175, 151 – 158. · Zbl 0596.73058
[8] Franco Brezzi and Michel Fortin, Mixed and hybrid finite element methods, Springer Series in Computational Mathematics, vol. 15, Springer-Verlag, New York, 1991. · Zbl 0788.73002
[9] Franco Brezzi, Michel Fortin, and Rolf Stenberg, Error analysis of mixed-interpolated elements for Reissner-Mindlin plates, Math. Models Methods Appl. Sci. 1 (1991), no. 2, 125 – 151. · Zbl 0751.73053 · doi:10.1142/S0218202591000083
[10] Todd Dupont and Ridgway Scott, Polynomial approximation of functions in Sobolev spaces, Math. Comp. 34 (1980), no. 150, 441 – 463. · Zbl 0423.65009
[11] L. Gastaldi, Uniform interior error estimates for Reissner-Mindlin plate model, Pubbl. IAN/CNR, N. 802, Pavia, 1991. · Zbl 0728.73044
[12] Lucia Gastaldi and Ricardo H. Nochetto, Quasi-optimal pointwise error estimates for the Reissner-Mindlin plate, SIAM J. Numer. Anal. 28 (1991), no. 2, 363 – 377. · Zbl 0728.73044 · doi:10.1137/0728020
[13] J. Necas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967.
[14] Joachim A. Nitsche and Alfred H. Schatz, Interior estimates for Ritz-Galerkin methods, Math. Comp. 28 (1974), 937 – 958. · Zbl 0298.65071
[15] R. Scholz, Optimal \?_{\infty }-estimates for a mixed finite element method for second order elliptic and parabolic problems, Calcolo 20 (1983), no. 3, 355 – 377 (1984). · Zbl 0571.65092 · doi:10.1007/BF02576470
[16] L. Ridgway Scott and Shangyou Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp. 54 (1990), no. 190, 483 – 493. · Zbl 0696.65007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.