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Punktweise Konvergenz der Methode der finiten Elemente beim Plattenproblem. (German) Zbl 0383.65061

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74K20 Plates
74S05 Finite element methods applied to problems in solid mechanics
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References:
[1] BABU?KA, I., ZLAMAL, M.: Nonconforming elements in the finite element method with penalty. SIAM J.Numer.Anal.10 863-875 (1973) · Zbl 0266.65071
[2] BRAMBLE, J.H., HILBERT, S.R.: Bounds on a class of linear functionals with applications to Hermite interpolation. Numer.Math.16, 362-369 (1971) · Zbl 0214.41405
[3] BREZZI, F.: On mixed finite element methods. Tagungsband ?Finite Elemente?, Bonn.Math.Schr. 1976 · Zbl 0371.65024
[4] CIARLET, P.G.: Conforming and nonconforming finite element methods for solving the plate problem. In ?Conf. Numerical Solution of Differential Equations?,University of Dundee 1973. Ed. G. A. Watson, Springer: Berlin-Heidelberg-New York 1974
[5] CIARLET, P.G., RAVIART, P.A.: The combined effect of curved boundaries and numerical integration in the isoparametric finite element method. Proc. of Conf. ?The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations?,University of Maryland 1972. Ed. A. K. Aziz, Academic Press: New York-London-San Francisco 1972
[6] CIARLET, P.G., RAVIART, P.A.: A mixed finite element method for the biharmonic operator. Proc.Symp. ?Mathematical Aspects of Finite Elements in Partial Differential Equations?, University of Wisconsin 1974. Ed. C. deBoor, Academic Press: New York-London-San Francisco 1974
[7] FREHSE, J., RANNACHER, R.: Eine L1-Fehlerabschätzung für diskrete Grundlösungen in der Methode der finiten Elemente. Tagungsband ?Finite Elemente?, Bonn.Math.Schr. 1976 · Zbl 0359.65093
[8] NE?AS, J.: Les méthodes directes en théorie des équations elliptiques. Masson: Paris 1967
[9] NITSCHE, J.: Convergence of nonconforming methods. Siehe [5]
[10] NITSCHE, J.: L?-convergence of finite element methods. Preprint of 2.Conf. ?Finite Elements?, Rennes, France 1975
[11] RANNACHER, R.: Zur L?-Konvergenz linearer finiter Elemente beim Dirichlet-Problem. Erscheint in der Math.Z. · Zbl 0321.65055
[12] SCHOLZ, R.: Approximation von Sattelpunkten mit finiten Elementen. Tagungsband ?Finite Elemente?, Bonn.Math. Schr. 1976 · Zbl 0359.65096
[13] STRANG, G., FIX, G.: An analysis of the finite element method. Prentice Hall: Englewood Cliffs 1973 · Zbl 0356.65096
[14] ZIENKIEWICZ, O.C.: The finite element method in engineering science. McGraw-Hill: London 1971 · Zbl 0237.73071
[15] ZLÁMAL, M.: Curved elements in the finite element method. I. SIAM J.Numer.Anal.10, 229-240 (1973), II. SIAM J. Numer.Anal.11, 347-362(1974) · Zbl 0285.65067
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