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Eigenvalue approximations by mixed methods. (English) Zbl 0434.65032

MSC:
65J10 Numerical solutions to equations with linear operators
49R50 Variational methods for eigenvalues of operators (MSC2000)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74H45 Vibrations in dynamical problems in solid mechanics
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References:
[1] 1. I. BABUSKA, The Finite Element Method with Lagrangian Multipliers, Num.Math., 20, 1973, pp. 179-192. Zbl0258.65108 · Zbl 0258.65108
[2] 2. I. BABUSKA and A. K. Aziz, Survey Lectures on the Mathematical Foundations of the Finite Element Method in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations; A. K, Aziz, Ed., Academic Press, NewYork 1972, pp. 3-359. Zbl0268.65052 · Zbl 0268.65052
[3] 3. I. BABUSKA, J. T. ODEN and J. K. LEE, Mixed-Hybrid Finite Element Approximations of Second Order Elliptic Boundary-Value Problems, TICOM Report 75-7, University of Texas at Austin, 1975. Zbl0382.65056 · Zbl 0382.65056
[4] 4. I. BABUSKA and J. E. OSBORN, Numerical Treatment of Eigenvalue Problems for Differential Equations with Discontinuous Coefficients, Technical Note BN-853, University of Maryland, College Park, 1977. Zbl0418.65053 · Zbl 0418.65053
[5] 5. G. BIRKHOFF, C. DE BOOR, B. SWARTZ and B. WENDROFF, Rayleigh-Ritz Approximation by Piecewise Cubic Polynomials, S.I.A.M. J. Num. Anal., 13, 1973 pp. 188-203. Zbl0143.38002 · Zbl 0143.38002
[6] 6. J. H. BRAMBLE and J. E. OSBORN, Rate of Convergence Estimates for Nonself-adjoint Eigenvalue Approximation, Math. of Comp., vol. 27, No. 123, 1973 pp. 525-549. Zbl0305.65064 · Zbl 0305.65064
[7] 7. F. BREZZI, On the Existence, Uniqueness and Approximations of Saddle-Point Problems Arising from Lagrangian Multipliers, R.A.I.R.O., R 2, août 1974, pp. 129-151. Zbl0338.90047 · Zbl 0338.90047
[8] 8. F. BREZZI and P. A. RAVIARTMixed Finite Element Methods for 4th Order Elliptic Equations, Rapport Interne No. 9, C.M.A. École Polytechnique, Palaiseau, 1976. MR657975
[9] 9. P. G. CIARLET and P. A. RAVIART, A Mixed Finite Element Method for the Biharmonic Equation Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations, C. DE BOOR, Ed., Academic Press, New York, 1974, pp. 125-145. Zbl0337.65058 MR657977 · Zbl 0337.65058
[10] 10. G. FIXEigenvalue Approximation by the Finite Element Method, Adv. in Math., 10, 1973, pp. 300-316. Zbl0257.65086 MR341900 · Zbl 0257.65086
[11] 11. R. GLOWINSKI, Approximations externes, par éléments finis de Lagrange d’ordre un et deux, du problème de Dirichlet pour l’opéraieur biharmonique. Méthode itérative de résolutions des problèmes approchés, Topics in Numerical Analysis, J. J. H. MILLER, Ed., Academic Press, London, 1973, pp. 123-171. Zbl0277.35003 MR351120 · Zbl 0277.35003
[12] 12. C. GOULAOUIC, Valeurs propres de problèmes aux limites irréguliers : applications, in Spectral Analysis, C.I.M.E. Session 1973, Cremonese, Rome, 1974, pp. 80-140.
[13] 13. V. A. KONDRAT’EV, Boundary Problems for Elliptic Equations in Domains with Conical or Angular Points, Trans. Moscow Math. Soc, vol. 16, 1967 pp. 227-313. Zbl0194.13405 MR226187 · Zbl 0194.13405
[14] 14. M. MERIGOT, Régularité des fonctions propres du laplacien dans un cône,C. R. Acad. Sc, Paris, 279, série A, 1974, pp. 503-505 Zbl0294.35060 MR377258 · Zbl 0294.35060
[15] 15. M. MERIGOT, Solutions en norme LP des problèmes élliptiques dans des polygônes plans, Thèse à l’Université de Nice, 1974.
[16] 16. J. E. OSBORN, Spectral Approximation for Compact Operators, Math, of Comp., 29, 1975, pp. 712-725 Zbl0315.35068 MR383117 · Zbl 0315.35068
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