@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: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {339--365}, publisher = {AFCET - Gauthier-Villars}, address = {Paris}, volume = {29}, number = {3}, year = {1995}, mrnumber = {1342711}, zbl = {0836.65113}, language = {en}, url = {http://www.numdam.org/item/M2AN_1995__29_3_339_0/} }
TY - JOUR AU - Vanmaele, M. AU - Van Keer, R. TI - An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1995 SP - 339 EP - 365 VL - 29 IS - 3 PB - AFCET - Gauthier-Villars PP - Paris UR - http://www.numdam.org/item/M2AN_1995__29_3_339_0/ LA - en ID - M2AN_1995__29_3_339_0 ER -
%0 Journal Article %A Vanmaele, M. %A Van Keer, R. %T An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures %J ESAIM: Modélisation mathématique et analyse numérique %D 1995 %P 339-365 %V 29 %N 3 %I AFCET - Gauthier-Villars %C Paris %U http://www.numdam.org/item/M2AN_1995__29_3_339_0/ %G en %F 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: Modélisation mathématique et analyse numérique, Tome 29 (1995) no. 3, pp. 339-365. http://www.numdam.org/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 | Zbl
, & ,[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 | Zbl
& ,[3] A note on the effect of numerical quadrature in finite element eigenvalue approximation, Numer. Math., 61, 1992, 145-152. | MR | Zbl
,[4] Estimation of the Effect of Numerical Integration in Finite Element Eigenvalue Approximation, Numer. Math., 56, 1990, 735-762. | MR | Zbl
& ,[5] Spectral Approximation of Linear Operators, New York : Academic Press, 1983. | MR | Zbl
,[6] The Finite Element Method for Elliptic Problems, Amsterdam : North-Holland, 1978. | MR | Zbl
,[7] Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, Tome 2. Paris : Masson, 1985. | MR | Zbl
& ,[8] Methods of numerical integration, New York : Academic Press, 1975. | MR | Zbl
& ,[9] On Spectral Approximation. Problem of Convergence, R.A.I.R.O. Numerical Analysis, 12, 1978, 97-112. | Numdam | MR | Zbl
, & ,[10] Eigenvalue Approximation by the Finite Element Method, Advances in Mathematics, 10, 1973, 300-316. | MR | Zbl
,[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
& ,[12] Finite Element Handbook, New York : McGraw-Hill Book Comp, 1987. | MR | Zbl
& ,[13] Perturbation Theory for Linear Operators, Berlin : Springer-Verlag, 1976. | MR | Zbl
,[14] Lectures on Topics in Finite Element Solution of Elliptic Problems, Berlin : Springer-Verlag, 1976. | Zbl
,[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 | Zbl
,[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 | Zbl
& ,[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 | Zbl
& ,