Approximation of eigenvalues of differential equations with non-smooth coefficients

Uday Banerjee

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 1, page 29-51
  • ISSN: 0764-583X

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Banerjee, Uday. "Approximation of eigenvalues of differential equations with non-smooth coefficients." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.1 (1988): 29-51. <http://eudml.org/doc/193512>.

@article{Banerjee1988,
author = {Banerjee, Uday},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {eigenvalues; eigenfunctions; finite element method; spectral approximation; error estimates; non-smooth coefficients},
language = {eng},
number = {1},
pages = {29-51},
publisher = {Dunod},
title = {Approximation of eigenvalues of differential equations with non-smooth coefficients},
url = {http://eudml.org/doc/193512},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Banerjee, Uday
TI - Approximation of eigenvalues of differential equations with non-smooth coefficients
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 1
SP - 29
EP - 51
LA - eng
KW - eigenvalues; eigenfunctions; finite element method; spectral approximation; error estimates; non-smooth coefficients
UR - http://eudml.org/doc/193512
ER -

References

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  1. [1] R. S. ANDERSSEN, J. R. CLEARY, Asymptotic Structure in Torsional Free Oscillations of Earth I. Geophys. J. R. Astr. Soc., 39, 1974, 241-268. Zbl0365.73095
  2. [2] I. BABUSKA, J. E. OSBORN, Numerical Treatment of Eigenvalue Problems for Differential Equations with Discontinuons Coefficients. Math. Comp., 32, 1978, 991-1023. Zbl0418.65053MR501962
  3. [3] I BABUSKA, J. E. OSBORN, Analysis of Finite Element Methods for Second Order Boundary Value Problems using Mesh Dependent Norms. Numer. Math., 34, 1980, 41-62. Zbl0404.65055MR560793
  4. [4] I. BABUSKA, J. E. OSBORN, Generalized Finite Element Methods : Their Performance and Their Relation to Mixed Methods. SIAM J. Numer. Anal., 20, 1983, 510-536. Zbl0528.65046MR701094
  5. [5] U. BANERJEE, Lower Norm Error Estimates for Approximate Solutions of Differential Equations with Non-Smooth Coefficients. Numer. Math, 51, 1987,303-321. Zbl0613.65087MR895089
  6. [6] U. BANERJEE, Approximation of Eigenvalues of Differential Equations with Rough Coefficients. Ph. D. thesis, 1985, Univ. of Md., College Park, MD 20742. 
  7. [7] J. H. BRAMBLE, J. E. OSBORN, Rate of Convergence Estimate for Non-Selfadjoint Eigenvalue Approximations. Math. Comp., 27, 1973, 523-549. Zbl0305.65064MR366029
  8. [8] F. CHATELIN, Spectral Approximation of Linear Operators, Academia Press, 1983. Zbl0517.65036MR716134
  9. [9] R. S. FALK, J. E. OSBORN, Error Estimates for Mixed Methods, R.A.I.R.O. Numer. Anal. 14, 1980, 249-277. Zbl0467.65062MR592753
  10. [10] S. K. GARG, V. SVALBONAS and G. A. GURTMAN, Analysis of structural Composite Materials, Marcel Dekker, NY, 1973. 
  11. [11] E. R. LAPWOOD, The Effect of Discontinuities in Density and Rigidity on Torsional Eigenfrequencies. Geophys. J. R. Astr. Soc., 1975, 40, 453-464. Zbl0297.73064
  12. [12] S. NEMAT-NASSER, General Variational Methods for Elastic Waves in Composities. J. Elasticity, 2, 1972, 73-90. 
  13. [13] S. NEMAT-NASSER, General Variational Principles in Nonlinear and Linear Elasticity with Applications. Mechanics Today, 1, 1974, 214-261. Zbl0305.73007
  14. [14] S. NEMAT-NASSER, F. FU, Harmonic Waves in Layered Composites ; Bounds on Eigenfrequencies, J. Appl. Mech., 41, 1974, 288-290. Zbl0296.73025
  15. [15] J. R. OSBORN, Spectral Approximation of Compact Operators. Math. Comp., 29, 1975, 712-725. Zbl0315.35068MR383117

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