External finite element approximations of eigenvalue problems

M. Vanmaele; A. Ženíšek

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1993)

  • Volume: 27, Issue: 5, page 565-589
  • ISSN: 0764-583X

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Vanmaele, M., and Ženíšek, A.. "External finite element approximations of eigenvalue problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 27.5 (1993): 565-589. <http://eudml.org/doc/193715>.

@article{Vanmaele1993,
author = {Vanmaele, M., Ženíšek, A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {ideal triangulation; finite element; second order elliptic eigenvalue problems; piecewise linear approximations; eigenfunctions; convergence},
language = {eng},
number = {5},
pages = {565-589},
publisher = {Dunod},
title = {External finite element approximations of eigenvalue problems},
url = {http://eudml.org/doc/193715},
volume = {27},
year = {1993},
}

TY - JOUR
AU - Vanmaele, M.
AU - Ženíšek, A.
TI - External finite element approximations of eigenvalue problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1993
PB - Dunod
VL - 27
IS - 5
SP - 565
EP - 589
LA - eng
KW - ideal triangulation; finite element; second order elliptic eigenvalue problems; piecewise linear approximations; eigenfunctions; convergence
UR - http://eudml.org/doc/193715
ER -

References

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  1. [1] I. BABUšKA, J. E. OSBORN, 1991, Eigenvalue Problems. In : Handbook of Numerical Analysis, Vol. II, Finite Element Methods (Part 1), (eds. Ciarlet, P. G. & Lions, J. L.), North-Holland, Amsterdam, pp. 641-787. Zbl0875.65087MR1115240
  2. [2] I. BABUšKA, J. E. OSBORN, 1989, Finite Element-Galerkin Approximation of the Eigenvalues and Eigenvectors of Selfadjoint Problems, Math. Comp., 52, 275-297. Zbl0675.65108MR962210
  3. [3] U. BANERJEE, J. E. OSBORN, 1990, Estimation of the Effect of Numerical Integration in Finite Element Eigenvalue Approximation, Numer. Math., 56, 735-762. Zbl0693.65071MR1035176
  4. [4] P. G. CIARLET, 1978, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam. Zbl0383.65058MR520174
  5. [5] M. FEISTAUER, A. Ženíšek, 1987, Finite Element Solution of Nonlinear Elliptic Problems, Numer. Math., 50, 451-475. Zbl0637.65107MR875168
  6. [6] R. GLOWINSKI, J. L. LIONS, R. TRÉMOLIERES, 1976, Analyse Numérique des Inéquations Variationnelles, Dunod, Paris. Zbl0358.65091
  7. [7] S. G. MIKHLIN, 1978, Partielle Differentialgleichungen in der Mathematischen Physik, Akademie Verlag, Berlin. Zbl0397.35001MR513026
  8. [8] J. NEČAS, 1967, Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris. MR227584
  9. [9] J. NEDOMA, 1978, The Finite Element Solution of Parabolic Equations, Appl. Math., 23, 408-438. Zbl0427.65075MR508545
  10. [10] L. A. OGANESIAN, L. A., RUKHOVEC, 1979, Variational Difference Methods for the Solution of Elliptic Problems, Izd. Akad. Nauk ArSSR, Jerevan. (In Russian). 
  11. [11] P.A. RAVIART, J. M. THOMAS, 1983, Introduction à l'Analyse Numérique des Equations aux Dérivées Partielles, Masson, Paris. Zbl0561.65069MR773854
  12. [12] A. Ženíšek, 1987, How to Avoid Green's Theorem in the Ciarlet-Raviart Theory of Variational Crimes, Modélisation Math. Anal. Numér., 21, 171-191. Zbl0623.65072MR882690
  13. [13] A. Ženíšek, 1990, Nonlinear Elliptic and Evolution Problems and their Finite Element Approximations, Academic Press, London. Zbl0731.65090MR1086876
  14. [14] M. ZLÁMAL, 1973, Curved Elements in the Finite Element Method I. SIAM J. Numer. Anal, 10, 229-240. Zbl0285.65067MR395263

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