Free Access
Issue
ESAIM: M2AN
Volume 36, Number 1, January/February 2002
Page(s) 1 - 32
DOI https://doi.org/10.1051/m2an:2002001
Published online 15 April 2002
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. I. Babuska and J.E. Osborn, Eigenvalue Problems, in Handbook of Numerical Analysis. Vol. II, P.G. Ciarlet and J.-L. Lions, Eds., in Finite Element Methods (Part 1), North-Holland Publishing Company, Amsterdam, New York, Oxford (1991) 641-787. [Google Scholar]
  3. S. Balasundaram and P.K. Bhattacharyya, On existence of solution of the Dirichlet problem of fourth-order partial differential equations with variable coefficients. Quart. Appl. Math. 39 (1983) 311-317. [Google Scholar]
  4. S. Balasundaram and P.K. Bhattacharyya, A mixed finite element method for fourth-order elliptic equations with variable coefficients. Comput. Math. Appl. 10 (1984) 245-256. [CrossRef] [MathSciNet] [Google Scholar]
  5. U. Banerjee, A note on the effect of numerical quadrature in finite element eigenvalue approximation. Numer. Math. 61 (1992) 145-152. [CrossRef] [MathSciNet] [Google Scholar]
  6. U. Banerjee and J.E. Osborn, Estimates of the effect of numerical integration in finite element eigenvalue approximation. Numer. Math. 56 (1990) 735-762. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Bernadou, Méthodes numériques pour les problèmes elliptiques, in Méthodes de Mathématiques Appliquées, Vol. 1, Chap. XI, C.E.A., France (1981). [Google Scholar]
  8. P.K. Bhattacharyya and N. Nataraj, Isoparametric Mixed Finite Element Approximation of Eigenvalues and Eigenvectors of 4th-Order Eigenvalue Problems with Variable Coefficients. Research Report No. R 98021, Laboratoire d' Analyse Numérique, Université de Paris VI (1998). [Google Scholar]
  9. P.K. Bhattacharyya and N. Nataraj, On Combined Effect of Boundary Approximation and Numerical Integration on Mixed Finite Element Solution of 4th order Elliptic Problems with Variable Coefficients. ESAIM: M2AN 133 (1999) 807-836. [CrossRef] [EDP Sciences] [Google Scholar]
  10. P.K. Bhattacharyya and N. Nataraj, Error Estimates for Isoparametric Mixed Finite Element Solution of 4th-Order Elliptic Problems with Variable Coefficients. In preparation. [Google Scholar]
  11. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. RAIRO Anal. Numér. 8 (1974) 129-151. [Google Scholar]
  12. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, Berlin, Heidelberg, New York (1991). [Google Scholar]
  13. F. Brezzi and P.A. Raviart, Mixed finite element methods for 4th-order elliptic equations. Topics Numer. Anal. III, J. Miller, Ed., Academic Press, New York (1978) 33-56. [Google Scholar]
  14. C. Canuto, Eigenvalue approximation by mixed methods. RAIRO Anal. Numér. 12 (1978) 27-50. [Google Scholar]
  15. F. Chatelin, Spectral Approximation of Linear Operators. Academic Press, New York (1983). [Google Scholar]
  16. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, Amsterdam, New York, Oxford (1978). [Google Scholar]
  17. P.G. Ciarlet and P.A. Raviart, The combined effect of curved boundaries and numerical integration in isoparametric finite element methods, in Math. Found. Finite El. Method Appl. Part. Differ. Equations, A.K. Aziz and I. Babuska, Eds., Sympos. Univ. Maryland, Baltimore (1972) 409-474. [Google Scholar]
  18. M. Dauge, Elliptic Boundary Value Problems on Corner Domains. Springer-Verlag, Berlin, Heidelberg, New York (1988). [Google Scholar]
  19. N.J. DeCapua and B.C. Sun, Transverse vibration of a class of orthotropic plates. J. Appl. Mech. (1972) 613-615. [Google Scholar]
  20. S. Gopalsamy and P.K. Bhattacharyya, On existence and uniqueness of solution of boundary value problems of fourth-order elliptic partial differential equations with variable coefficients. J. Math. Anal. Appl. 136 (1988) 589-608. [CrossRef] [MathSciNet] [Google Scholar]
  21. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985). [Google Scholar]
  22. K. Ishihara, A mixed finite element method for the biharmonic eigenvalue problem of plate bending. Publ. Res. Inst. Math. Sci. Kyoto Univ. 14 (1978) 399-414. [CrossRef] [Google Scholar]
  23. K. Ishihara, The buckling of plates by the mixed finite element method. Mem. Numer. Math. 5 (1978) 73-82. [Google Scholar]
  24. V.A. Kondratev, Boundary value problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Obshch. 16 (1967) 209-292. [Google Scholar]
  25. M.P. Lebaud, Error estimate in an isoparametric finite element Eigenvalue Problem. Math. Comp. 63 (1994) 19-40. [CrossRef] [MathSciNet] [Google Scholar]
  26. A.W. Leissa, Vibration of Plates. NASA SP-160 (1969). [Google Scholar]
  27. S.G. Leknitskii, Anisotropic Plates. Gordon and Breach Science Publishers, New York (1968). [Google Scholar]
  28. J.-L. Lions, Problèmes aux limites dans les équations aux dérivées partielles. Presses Univ. Montréal, Montreal (1965). [Google Scholar]
  29. B. Mercier, J. Osborn, J. Rappaz and P.A. Raviart, Eigenvalue approximation by mixed and hybrid methods. Math. Comp. 36 (1981) 427-453. [CrossRef] [MathSciNet] [Google Scholar]
  30. T. Miyoshi, A finite element method for the solution of fourth-order partial differential equations. Kumamoto J. Sci. (Math.) 9 (1973) 87-116. [Google Scholar]
  31. N. Nataraj, On Mixed Finite Element Analysis Of Fourth Order Elliptic Source/Eigenvalue Problems in Convex Domains. Ph.D. Thesis, Dept. of Mathematics, Indian Institute of Technology, Delhi (1998). [Google Scholar]
  32. L.A. Oganesian and L.A. Rukhovec, Variational difference methods for the solution of elliptic problems. Izv. Akad. Nauk Armyan. SSR, Yerevan (1979). In Russian. [Google Scholar]
  33. A.B. Ouaritini, Méthodes d'éléments finis mixtes pour des problèmes de coques minces. Thèse de Docteur de 3e cycle, Université de Pau et des Pays de L'Adour, France (1984). [Google Scholar]
  34. O. Pironneau, Méthodes des éléments finis pour les fluides. Masson, Paris (1988). [Google Scholar]
  35. P.A. Raviart and J.M. Thomas, Introduction à l'analyse numérique des équations aux dérivées partielles. Masson, Paris (1983). [Google Scholar]
  36. J.E. Roberts and J.M. Thomas, Mixed and Hybrid Methods, in Handbook of Numerical Analysis. Vol. II, in Finite Element Methods (Part 1), P.G. Ciarlet and J.-L. Lions, Eds., North-Holland Publishing Company, Amsterdam, New York, Oxford, (1991) 523-633. [Google Scholar]
  37. G. Strang and G.J. Fix, An Analysis of the Finite Element Method. Prentice-Hall, New York (1973). [Google Scholar]
  38. S. Timoshenko and S. Woinowsky-Kreiger, Theory of Plates and Shells. McGraw-Hill Book Company, New York (1959). [Google Scholar]
  39. M. Vanmaele and A. Zenísek, External finite-element approximations of eigenvalue problems. RAIRO Modél. Math. Anal. Numér. 27 (1993) 565-589. [MathSciNet] [Google Scholar]
  40. M. Vanmaele and A. Zenísek, The combined effect of numerical integration and approximation of boundary in the finite element method for eigenvalue problems. Numer. Math. (1995). [Google Scholar]
  41. A. Zenísek, Nonlinear Elliptic and Evolution Problems and their Finite Element Approximations. Academic Press, New York (1990). [Google Scholar]

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