Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients

Pulin Kumar Bhattacharyya; Neela Nataraj

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 1, page 1-32
  • ISSN: 0764-583X

Abstract

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Estimates for the combined effect of boundary approximation and numerical integration on the approximation of (simple) eigenvalues and eigenvectors of 4th order eigenvalue problems with variable/constant coefficients in convex domains with curved boundary by an isoparametric mixed finite element method, which, in the particular case of bending problems of aniso-/ortho-/isotropic plates with variable/constant thickness, gives a simultaneous approximation to bending moment tensor field Ψ = ( ψ i j ) 1 ≤ i , j ≤ 2 and displacement field ‘u’, have been developed.

How to cite

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Bhattacharyya, Pulin Kumar, and Nataraj, Neela. "Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.1 (2002): 1-32. <http://eudml.org/doc/245988>.

@article{Bhattacharyya2002,
abstract = {Estimates for the combined effect of boundary approximation and numerical integration on the approximation of (simple) eigenvalues and eigenvectors of 4th order eigenvalue problems with variable/constant coefficients in convex domains with curved boundary by an isoparametric mixed finite element method, which, in the particular case of bending problems of aniso-/ortho-/isotropic plates with variable/constant thickness, gives a simultaneous approximation to bending moment tensor field $\Psi = (\psi _\{ij\})_\{1 \le i,j \le 2\}$ and displacement field ‘u’, have been developed.},
author = {Bhattacharyya, Pulin Kumar, Nataraj, Neela},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mixed FEM; eigenvalue problem; isoparametric boundary approximation; 4th-order equations; anisotropic plates; convergence analysis; numerical results},
language = {eng},
number = {1},
pages = {1-32},
publisher = {EDP-Sciences},
title = {Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients},
url = {http://eudml.org/doc/245988},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Bhattacharyya, Pulin Kumar
AU - Nataraj, Neela
TI - Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 1
SP - 1
EP - 32
AB - Estimates for the combined effect of boundary approximation and numerical integration on the approximation of (simple) eigenvalues and eigenvectors of 4th order eigenvalue problems with variable/constant coefficients in convex domains with curved boundary by an isoparametric mixed finite element method, which, in the particular case of bending problems of aniso-/ortho-/isotropic plates with variable/constant thickness, gives a simultaneous approximation to bending moment tensor field $\Psi = (\psi _{ij})_{1 \le i,j \le 2}$ and displacement field ‘u’, have been developed.
LA - eng
KW - mixed FEM; eigenvalue problem; isoparametric boundary approximation; 4th-order equations; anisotropic plates; convergence analysis; numerical results
UR - http://eudml.org/doc/245988
ER -

References

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