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Finite element approximations of the von Kármán equations. (English) Zbl 0398.73070

MSC:
74K20 Plates
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:
[1] 1. T. VON KARMAN, Festigkeitsprobleme in Maschinbau, Encycl. der Math. Wissenschaften, vol. 4, 1910, pp. 348-352.
[2] 2. M. S. BERGER, On von Kármán Equations and the Buckling of a thin Elastic Plate, Comm. Pure Appl. Math., vol. 20, 1967, pp. 687-718. Zbl0162.56405 MR221808 · Zbl 0162.56405 · doi:10.1002/cpa.3160200405
[3] 3. T. MIYOSHI, A Mixed Finite Element Method for the Solution of the von Kármán Equations, Num. Math., vol. 26, 1976, pp. 255-269. Zbl0315.65064 MR438741 · Zbl 0315.65064 · doi:10.1007/BF01395945 · eudml:132413
[4] 4. A. GOBETTI and L. D. MARINI, to appear.
[5] 5. H. B. KELLER, Approximation Methods for Nonlinear Problems with Applications to two-Point Boundary Value Problems, Math. Comp., vol. 29, 1975, pp. 464-474. Zbl0308.65039 MR371058 · Zbl 0308.65039 · doi:10.2307/2005564
[6] 6. J. NE_AS, Les Méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. · Zbl 1225.35003
[7] 7. I. BABUSKA, Error Bound for the Finite Element Method, Num. Math., vol. 16, 1971, pp. 322-333. Zbl0214.42001 MR288971 · Zbl 0214.42001 · doi:10.1007/BF02165003 · eudml:132037
[8] 8. P. G. CIARLET and P. A. RAVIART, General Lagrange and Hermite interpolation in R n with applications to finite element methods, Arch. Rat. Mech. Anal., vol. 46, 1972, pp. 177-199. Zbl0243.41004 MR336957 · Zbl 0243.41004 · doi:10.1007/BF00252458
[9] 9. G. STRANG and G. FIX, An Analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, 1973. Zbl0356.65096 MR443377 · Zbl 0356.65096
[10] 10. P. G. CIARLET, The Finite Element Method for Elliptic Problems, North Holland, Amsterdam, 1977. Zbl0383.65058 MR520174 · Zbl 0383.65058
[11] 11. S. G. MIKHLIN, The Numerical Performance of Variational Methods, Wolters Noordholf, Groningen, 1971. Zbl0209.18301 MR278506 · Zbl 0209.18301
[12] 12. A. L. SCHATZ, An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms, Math, of Comp., vol. 28, 1974, pp. 959-962. Zbl0321.65059 MR373326 · Zbl 0321.65059 · doi:10.2307/2005357
[13] 13. D. J. ALLMAN, Some Fundamental Aspects of the Finite Element Analysis of Nonlinear Elastic Plate Bending, Finite Elements in Nonlinear Solid and Structural Mechanics, Geilo (Norway), August 29-Sept 1, 1977, pp. C. 06. Zbl0424.73069 · Zbl 0424.73069
[14] 14. J. L. LIONS and E. MAGENES, Problèmes aux limites non homogènes et applications, vol.1, Dunod, Paris, 1968. Zbl0165.10801 MR247243 · Zbl 0165.10801
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