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On the convergence of a mixed finite-element method for plate bending problems. (English) Zbl 0264.65070

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
74B99 Elastic materials
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References:
[1] Allman, D. J.: Triangular finite elements for plate bending with constant and linearly varying bending moments. Colloqium of the International Union of Theoretical and Applied Mechanics (IUTAM) on High Speed Computing of Elastic Structures, University of Liege, Belgium, August 23-28, 1970.
[2] Bramble, J., Hilbert, S. R.: Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and Spline interpolation. Siam. J. Numer. Anal.7, 112-124 (1970). · Zbl 0201.07803 · doi:10.1137/0707006
[3] Bramble, J., Zlamal, M.: Triangular elements in the finite element method. Math. Comp.,24, 809-820 (1970). · doi:10.1090/S0025-5718-1970-0282540-0
[4] Hellan, K.: Analysis of elastic plates in flexure by a simplified finite element method. Acta Polytechnica Scandinavica, Ci 46, Trondheim, 1967. · Zbl 0237.73046
[5] Herrmann, L.: Finite element bending analysis for plates. J. of Mech., Div. ASCE, a 3, EM 5, 1967.
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[8] Lions, J. L., Magenes, E.: Problemes aux limites non homogenes et applications. Vol. 1, Travaux Recherches Math., no. 17. Paris: Dunod 1968. · Zbl 0165.10801
[9] Necas, J.: Les methodes directes en theorie des equations elliptiques. Paris: Masson 1967.
[10] Mikhlin, S. G.: Variational methods in mathematical physics. Berlin: Akademie Verlag 1962. · Zbl 0116.33103
[11] Strang, G., Fix, G.: An analysis of the finite element method. Prentice-Hall, Inc. (to appear). · Zbl 0356.65096
[12] Synge, J. L.: The hypercircle in mathematical physics. Cambridge at the University Press 1957. · Zbl 0079.13802
[13] Visser, W.: A refined mixed type plate bending element. A.I.A.A. Journal7, 1969. · Zbl 0194.26601
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