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Une methode d’elements finis mixte pour les equations de von Kármán. (German) Zbl 0451.73053


MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
49R50 Variational methods for eigenvalues of operators (MSC2000)
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References:

[1] 1. L BAUER et E REISS, Non Linear Buckling of Rectangular PlatesBuckhng of Rectangular Plates, SIAM, Num Anal, vol 13, 1965, p 603-627.
[2] 2. F BREZZI, On the Existence, Uniqueness and Approximation of Saddle-PointProblems Arising from Lagrangian Multipliers, RAIRO , Analyse numérique,of R-2, 1974, p 129-151. Zbl0338.90047 MR365287 · Zbl 0338.90047
[3] 3. F. BREZZI et P. A. RAVIART, Mixed Finite Element Methods for Fourth Order EllipticEquations, Rapport Interne, n^\circ 9, École Polytechnique, Palaiseau, 1976.
[4] 4. C. CANUTO, Eigenvalue Approximations by Mixed Methods, R.A.I.R.O., Analyse numérique, vol. 12, 1978, p. 27-50. Zbl0434.65032 MR488712 · Zbl 0434.65032
[5] 5. P. G. CIARLET, TheFinite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. Zbl0383.65058 MR520174 · Zbl 0383.65058
[6] 6. P. G. CIARLET, Derivation of the von Karman Equations from Three-Dimensional Elasticity, Proceedings of the Fourth Conference on Basic Problems in Numerical Analysis, Plzen, 1978 (à paraître). Zbl0445.73043 MR566153 · Zbl 0445.73043
[7] 7. P. G. CIARLET et P. A. RAVIART, A Mixed Finite Element Method for the Biharmonic Equation in Mathematical Aspects of ’Finite Eléments in Partial Differentiat Equations, C. DE BOOR, éd. 1974, p. 125-145. Zbl0337.65058 MR657977 · Zbl 0337.65058
[8] 8. S. KESAVAN, Homogenization of Elliptic Eigenvalue Problems, Applied Mathematicsand Optimizalion. vol. 5, n^\circ 2, 1979, p. 153-167. Zbl0415.35061 MR533617 · Zbl 0415.35061 · doi:10.1007/BF01442551
[9] 9. S. KESAVAN, La méthode de Kikuchi appliquée aux équations de von Karman, Numerische Mathematik, vol.32, 1979, p. 209-232. Zbl0395.73054 MR529910 · Zbl 0395.73054 · doi:10.1007/BF01404876
[10] 10. S. KESAVAN et M. VANNINATHAN, Sur une méthode d’éléments finis mixte pour l’équation biharmonique, R.A.I.R.O., Analyse numérique, vol. 11, n^\circ 3, 1977, p. 255-270. Zbl0372.65039 MR451777 · Zbl 0372.65039
[11] 11. F. KIKUCHI, An Iterative Finite Element Scheme for Bifurcation Analysis of Semi-Linear Elliptic Equations, Report n^\circ 542, Institute of space and Aeronautical Science,Univ. of Tokyo, Japan, 1976.
[12] 12. V. A. KONDRAT’EV, Boundary Value Problems for Elliptic Equations in Domains with Conical or Angular Points, Trudy Moskov. Mat.Obsc, vol. 16, 1967, p. 209-292. Zbl0162.16301 MR226187 · Zbl 0162.16301
[13] 13. B. MERCIER et J. RAPPAZ, Eigenvalue Approximation via Non-Conforming and Hybrid Finite Element Methods, Rapport Interne, n^\circ 33, École Polytechnique, Palaiseau, 1978.
[14] 14. T. MIYOSHI, Finite Element Method for the Solution of Fourth Order Partial Differential Equations, Kumamoto J. Se. (Math.), vol.9, 1973, p. 87-116. Zbl0249.35007 MR386298 · Zbl 0249.35007
[15] 15. R. RANNACHER, Non Conforming Finite Element Methods for Eigenvalue Problems in Linear Plate Theory, Preprint, n^\circ 191, Univ. of Bonn, W. Germany, 1978. Zbl0394.65035 · Zbl 0394.65035 · doi:10.1007/BF01396493
[16] 16. R. RANNACHER, On Non-Conforming and Mixed Finite Element Methods for Plate Bending Problems, Thelinear case, R.A.I.R.O., Analyse numérique (à paraître). Zbl0425.35042 · Zbl 0425.35042
[17] 17. R. SCHOLZ, Approximation von Sattelpunkten mit Finiten Elementen, Bonner Math.Schrifter, vol. 89, 1976, p. 53-66. Zbl0359.65096 MR471377 · Zbl 0359.65096
[18] 18. G. STRANG et G. J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Inc. Englewood Cliffs, 1973. Zbl0356.65096 MR443377 · Zbl 0356.65096
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