A hybrid finite element method to compute the free vibration frequencies of a clamped plate
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 15 (1981) no. 2, p. 101-118
@article{M2AN_1981__15_2_101_0,
author = {Canuto, Claudio},
title = {A hybrid finite element method to compute the free vibration frequencies of a clamped plate},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {Dunod},
volume = {15},
number = {2},
year = {1981},
pages = {101-118},
zbl = {0462.73049},
mrnumber = {618818},
language = {en},
url = {http://www.numdam.org/item/M2AN_1981__15_2_101_0}
}

Canuto, Claudio. A hybrid finite element method to compute the free vibration frequencies of a clamped plate. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 15 (1981) no. 2, pp. 101-118. http://www.numdam.org/item/M2AN_1981__15_2_101_0/

1 P M. Anselone, Collectively Compact Operator Approximation Theory to Integral Equations, Prentice Hall, Englewood Cliffs, N.J., 1971. | MR 443383 | Zbl 0228.47001

2 K. Brandt, Calculation of vibration frequencies by a hybrid element method based on a generalized complementary energy principle, Int. J num. Meth. Engng., v. 12, 1977, pp. 231-246. | Zbl 0346.73054

3. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, R.A.I.R.O , R-2, 1974, pp 129-151. | Numdam | MR 365287 | Zbl 0338.90047

4 F. Brezzi, Sur la méthode des éléments finis hybrides pour le problème biharmonique, Num. Math. v 24, 1975, pp. 103-131. | MR 391538 | Zbl 0316.65029

5. F Brezzi and L. D. Marini, On the numerical solution of plate bending problems by hybrid methods, R.A.I.R.O., R-3, 1975, pp. 5-50. | Numdam | Zbl 0322.73048

6 C Canuto, Eigenvalue approximations by mixed methods, R.A.I.R.O. Anal Num., v. 12, 1978, pp. 27-50 | Numdam | MR 488712 | Zbl 0434.65032

7. C. Canuto, A finite element to interpolate symmetric tensors with divergence in ${L}^{2}$ (To appear on Calcolo). | Zbl 0508.65051

8. P G Ciarlet, The finite element method for elliptic problems, North-Holland, Amsterdam-New York-Oxford, 1978. | MR 520174 | Zbl 0383.65058

9. G. Fichera, Numerical and Quantitative Analysis, Pitman, London-San Francisco-Melbourne, 1978. | MR 519677 | Zbl 0384.65043

10. P. Grisvard, Singularité des solutions du problème de Stokes dans un polygone (To appear)

11 W. G. Kolata, Eigenvalue approximation by the finite element method : the method of Lagrange multipliers (To appear) | MR 514810 | Zbl 0448.65067

12 V. A. Kondrat'Ev, Boundary problems for elliptic equations in domains with conical or angular points, Trans Moscow Math Soc., v 16, 1976, pp 227-313. | Zbl 0194.13405

13. B. Mercier and J. Rappaz, Eigenvalue approximation via nonconforming and hybrid finite elements methods, Rapport Interne du Centre de Mathématiques Appliquées de l'École Polytechnique, n° 33, 1978

14. B. Mercier, J. Osborn, J. Rappaz and P.-A. Raviart, Eigenvalue approximation by mixed and hybrid methods (To appear). | MR 606505 | Zbl 0472.65080

15. T. H. H. Piang and P. Tong, The basis of finite element methods for solid continua, Int. J. num. Meth. Engng., v. 1, 1969, pp. 3-28. | Zbl 0252.73052

16. J. Rappaz, Approximation of the spectrum of a non-compact operator given by the magnetohydrodynamic stability of a plasma, Num. Math., v. 28, 1977, pp. 15-24. | MR 474800 | Zbl 0341.65044

17. J. Rappaz, Spectral approximation by finite elements of a problem of MHD-stability of a plasma, The Mathematics of Finite Elements and Applications III, MAFELAP 1978 (Ed. J. R. Whiteman), Academic Press, London-New York-San Francisco, 1979, pp. 311-318. | MR 559307 | Zbl 0442.76087

18. G. Strang and G. Fix, An Analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, N.J., 1973. | MR 443377 | Zbl 0356.65096

19. B. Tabarrok, A variational principle for the dynamic analysis of continua by hybrid finite element method, Int. J. Solids Struct., v. 7, 1971, pp. 251-268. | Zbl 0228.73053

20. R. A. Toupin, A variational principle for the mesh-type analysis of the mechanical system, Trans. Am. Soc. Mech. Engngs., v. 74, 1952, pp. 151-152. | MR 51053 | Zbl 0047.17710

21. P. G. Gilardi (To appear).