Vanmaele, M.; Van Keer, R.
An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 29 (1995) no. 3 , p. 339-365
Zbl 0836.65113 | MR 1342711
URL stable : http://www.numdam.org/item?id=M2AN_1995__29_3_339_0

Bibliographie

[1] A. B. Andreev, V. A. Kascieva & M. Vanmaele, Some results in lumped, mass finite-element approximation of eigenvalue problems using numerical quadrature, J. Comp. Appl. Math., 43, 1992, 291-311. MR 1193808 | Zbl 0762.65056

[2] I. Babuška & J. E. Osborn, Eigenvalue Problems. In : Handbook of Numerical Analysis, Vol. II, Finite Element Methods (Part 1) (P. G. Ciarlet, J. L. Lions, eds.). Amsterdam: North-Holland, 1991, 641-787. MR 1115240 | Zbl 0875.65087

[3] U. Banerjee, A note on the effect of numerical quadrature in finite element eigenvalue approximation, Numer. Math., 61, 1992, 145-152. MR 1147574 | Zbl 0748.65078

[4] U. Banerjee & J. E. Osborn, Estimation of the Effect of Numerical Integration in Finite Element Eigenvalue Approximation, Numer. Math., 56, 1990, 735-762. MR 1035176 | Zbl 0693.65071

[5] F. Chatelin, Spectral Approximation of Linear Operators, New York : Academic Press, 1983. MR 716134 | Zbl 0517.65036

[6] P. G. Ciarlet, The Finite Element Method for Elliptic Problems, Amsterdam : North-Holland, 1978. MR 520174 | Zbl 0383.65058

[7] R. Dautray & J.-L. Lions, Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, Tome 2. Paris : Masson, 1985. MR 902801 | Zbl 0749.35005

[8] R J. Davis & P. Rabinowitz, Methods of numerical integration, New York : Academic Press, 1975. MR 448814 | Zbl 0304.65016

[9] J. Descloux, N. Nassif & J. Rappaz, On Spectral Approximation. Problem of Convergence, R.A.I.R.O. Numerical Analysis, 12, 1978, 97-112. Numdam | MR 483400 | Zbl 0393.65024

[10] G. J. Fix, Eigenvalue Approximation by the Finite Element Method, Advances in Mathematics, 10, 1973, 300-316. MR 341900 | Zbl 0257.65086

[11] J. Kačur & R. Van Keer, On the Numerical Solution of some Heat Transfer Problems in Multi-component Structures with Non-perfect Thermal Contacts. In : Numerical Methods for Thermal Problems VII (R. W. Lewis, ed.). Swansea : Pineridge Press, 1991, 1378-1388. MR 1132506

[12] H. Kardestuncer & D. H. Norrie, Finite Element Handbook, New York : McGraw-Hill Book Comp, 1987. MR 900813 | Zbl 0638.65076

[13] T. Kato, Perturbation Theory for Linear Operators, Berlin : Springer-Verlag, 1976. MR 407617 | Zbl 0342.47009

[14] B. Mercier, Lectures on Topics in Finite Element Solution of Elliptic Problems, Berlin : Springer-Verlag, 1976. Zbl 0445.65100

[15] M. N. Özisik, Heat Conduction, New York John Wiley & Sons, 1980.

[16] M. Vanmaele, On optimal and nearly optimal error estimates of a numerical quadrature finite element method for 2nd-order eigenvalue problems with Dirichlet boundary conditions, Simon Stevin, 67, 1992, 121-132. MR 1249049 | Zbl 0802.65106

[17] M. Vanmaele, A numerical quadrature finite element method for 2nd-order eigenvalue problems with Dirichlet-Robin boundary conditions. Proceedings ISNA '92. Prague, 1994, 269-292.

[18] M. Vanmaele & R. Van Keer, Error estimates for a finite element method with numerical quadrature for a class of elliptic eigenvalue problems. In : Numerical Methods (D. Greenspan, R Rósza, eds.). Colloq. Math. Soc. János Bolyai, 59, 1990, Amsterdam, North-Holland, 267-282. MR 1161236 | Zbl 0760.65096

[19] M. Vanmaele & R. Van Keer, On a numerical quadrature finite element method for a class of elliptic eigenvalue problems in composite structures, Math. Comp.(submitted).

[20] M. Vanmaele & A. Ženišek, External finite element approximations of eigen-functions in case of multiple eigenvalues. J. Comp. Appl. Math. 50 (to appear). MR 1284251 | Zbl 0811.65090