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Construction of basic functions for numerical utilisation of Ritz’s method. (English) Zbl 0271.65061

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:
[1] Mikhlin, S. G.: Variational methods in mathematical physics. New York: Macmillan 1964. · Zbl 0119.19002
[2] Engeli, M., Th. Ginsburg, H. Rutishauser, andE. Stiefel: Refined iterative methods for computation of the solution and the eigenvalues of self-adjoint boundary value problems. Mitteilungen aus dem Institut für angewandte Mathematik, Nr. 8, Zürich, 1959 · Zbl 0089.12103
[3] Courant, R.: Variational methods for the solution of problems of equilibrium and vibrations. Bull. Amer. Math. Soc.49, 1–23 (1943). · Zbl 0063.00985 · doi:10.1090/S0002-9904-1943-07818-4
[4] 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., Wright Patterson A.F. Base, Ohio, 1965.
[5] Zienkiewicz, O. C.: The finite element method in structural and continuum mechanics. New York: McGraw Hill 1967. · Zbl 0189.24902
[6] Ciarlet, P. G., M. H. Schultz, andR. S. Varga: Numerical methods of highorder accuracy for nonlinear boundary value problems. I. One dimensional problem. Numerische Mathematik9, 394–430 (1967). · Zbl 0155.20403 · doi:10.1007/BF02162155
[7] Schultz, M. H., andR. S. Varga:L-splines. Numerische Mathematik10, 345–369 (1967). · Zbl 0183.44402 · doi:10.1007/BF02162033
[8] Birkhoff, G., M. H. Schultz, andR. S. Varga: Piecewise Hermite interpolation in one and two variables with applications to partial differential equations. Numerische Mathematik11, 232–256 (1968). · Zbl 0159.20904 · doi:10.1007/BF02161845
[9] Goël, J.-J.: Utilisation numérique de la méthode de Ritz, application au calcul de plaque, thèse de doctorat. Ecole polytechnique de l’Université de Lausanne, 1968.
[10] - List of basic functions for numerical utilisation of Ritz’s method, application to the problem of the plate. Ecole polytechnique de l’Université de Lausanne, 1968.
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