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On the finite element method. (English) Zbl 0176.16001


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

[1] Aubin, J.-P.: Approximation des espaces de distributions et des opérateurs differentiels. Bull. Soc. Math. France, Mémoire12 (1967). · Zbl 0157.21901
[2] Berezin, I. S., andN. P. Židkov: Computing methods, vol. I. English translation. Oxford: Pergamon Press 1965.
[3] Birkhoff, G., M. H. Schultz, andR. S. Varga: Piecewise Hermite interpolation in one and two variables with applications to partial differential equations. Numer. Math.11, 232–256 (1968). · Zbl 0159.20904
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[5] Ciarlet, P. G.: Variational methods for non-linear boundary value problems. Thesis, Case Institute of Technology, June 1966.
[6] —-M. H. Schultz, andR. S. Varga: Numerical methods of high-order accuracy for nonlinear boundary value problems. I. One dimensional problem. Numer. Math.9, 394–430 (1967). · Zbl 0155.20403
[7] Clough, R. W., andJ. L. Tocher: Finite element stiffness matrices for analysis of plates in bending. Proc. Conf. Matrix Methods in Struct. Mech., Air Force Inst. of Tech., Dayton, Ohio, Oct. 1965.
[8] Courant, R.: Variational methods for the solution of problems of equilibrium and vibrations. Bull. Amer. Math. Soc.49, 1–23 (1943). · Zbl 0063.00985
[9] Fraeijs de Veubeke, B.: Displacement and equilibrium models in the finite element method, chap. 9 of Stress analysis, ed. O. C. Zienkiewicz and G. S. Holister. London: Wiley 1965.
[10] —-: A conforming finite element for plate bending. Int. J. Solids Structures4, 95–108 (1968). · Zbl 0168.22602
[11] Friedrichs, K.: Die Randwert- und Eigenwertprobleme aus der Theorie der elastischen Platten. Anwendung der direkten Methoden der Variationsrechnung. Math. Annalen98, 205–247 (1928). · JFM 53.0469.03
[12] Friedrichs, K. O., andH. B. Keller: A finite difference scheme for generalized Neumann problems. Numerical solution of partial differential equations. Proceedings of a Symposium held at the University of Maryland, ed. byJ. H. Bramble. New York: Academic Press 1966. · Zbl 0147.13901
[13] Michlin, S. G., andH. L. Smolickii: Approximate methods for solution of differential and integral equations. English translation. New York: Elsevier 1967.
[14] Oganesjan, L. A.: Convergence of difference schemes in case of improved approximation of the boundary. [In Russian.] Ž. Vyčisl. Mat. i Mat. Fiz.6, 1029–1042 (1966). · Zbl 0176.15604
[15] Smirnov, V. I.: A course in higher mathematics, vol. V. English translation. Oxford: Pergamon Press 1964. · Zbl 0121.25904
[16] Varga, R. S.: Hermite interpolation-type Ritz methods for two-point boundary value problems. Numerical solution of partial differential equations. Proceedings of a Symposium held at the University of Maryland, ed. byJ. H. Bramble. New York: Academic Press 1966. · Zbl 0161.35701
[17] Zienkiewicz, O. C.: The finite element method in structural and continuum mechanics. London: McGraw Hill 1967. · Zbl 0189.24902
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