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

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
74B99Elastic materials
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.
[5]Herrmann, L.: Finite element bending analysis for plates. J. of Mech., Div. ASCE, a 3, EM 5, 1967.
[6]Kondratev, V. A.: Boundary value problems for elliptic equations with conical or angular points. Trans. Moscow Math. Soc., 1967, pp. 227-313.
[7]Kufner, A.: Einige Eigenschaften der Sobolevschen Räume mit Belegungsfunktion. Czech. Math. J.15, 597-620 (1965).
[8]Lions, J. L., Magenes, E.: Problemes aux limites non homogenes et applications. Vol. 1, Travaux Recherches Math., no. 17. Paris: Dunod 1968.
[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.
[11]Strang, G., Fix, G.: An analysis of the finite element method. Prentice-Hall, Inc. (to appear).
[12]Synge, J. L.: The hypercircle in mathematical physics. Cambridge at the University Press 1957.
[13]Visser, W.: A refined mixed type plate bending element. A.I.A.A. Journal7, 1969.