@article{M2AN_1995__29_3_339_0, author = {Vanmaele, M. and Van Keer, R.}, title = {An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {29}, year = {1995}, pages = {339-365}, mrnumber = {1342711}, zbl = {0836.65113}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_1995__29_3_339_0} }
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) pp. 339-365. http://gdmltest.u-ga.fr/item/M2AN_1995__29_3_339_0/
[1] 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] 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] 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] Estimation of the Effect of Numerical Integration in Finite Element Eigenvalue Approximation, Numer. Math., 56, 1990, 735-762. | MR 1035176 | Zbl 0693.65071
& ,[5] Spectral Approximation of Linear Operators, New York : Academic Press, 1983. | MR 716134 | Zbl 0517.65036
,[6] The Finite Element Method for Elliptic Problems, Amsterdam : North-Holland, 1978. | MR 520174 | Zbl 0383.65058
,[7] Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, Tome 2. Paris : Masson, 1985. | MR 902801 | Zbl 0749.35005
& ,[8] Methods of numerical integration, New York : Academic Press, 1975. | MR 448814 | Zbl 0304.65016
& ,[9] On Spectral Approximation. Problem of Convergence, R.A.I.R.O. Numerical Analysis, 12, 1978, 97-112. | Numdam | MR 483400 | Zbl 0393.65024
, & ,[10] Eigenvalue Approximation by the Finite Element Method, Advances in Mathematics, 10, 1973, 300-316. | MR 341900 | Zbl 0257.65086
,[11] 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] Finite Element Handbook, New York : McGraw-Hill Book Comp, 1987. | MR 900813 | Zbl 0638.65076
& ,[13] Perturbation Theory for Linear Operators, Berlin : Springer-Verlag, 1976. | MR 407617 | Zbl 0342.47009
,[14] Lectures on Topics in Finite Element Solution of Elliptic Problems, Berlin : Springer-Verlag, 1976. | Zbl 0445.65100
,[15] Heat Conduction, New York John Wiley & Sons, 1980.
,[16] 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] A numerical quadrature finite element method for 2nd-order eigenvalue problems with Dirichlet-Robin boundary conditions. Proceedings ISNA '92. Prague, 1994, 269-292.
,[18] 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] On a numerical quadrature finite element method for a class of elliptic eigenvalue problems in composite structures, Math. Comp.(submitted).
& ,[20] External finite element approximations of eigen-functions in case of multiple eigenvalues. J. Comp. Appl. Math. 50 (to appear). | MR 1284251 | Zbl 0811.65090
& ,