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 (2010)

  • 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 36.1 (2010): 1-32. <http://eudml.org/doc/194094>.

@article{Bhattacharyya2010,
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},
keywords = {Mixed FEM; eigenvalue problem; isoparametric boundary approximation; 4th-order equations; anisotropic plates; convergence analysis; numerical results.; mixed FEM; numerical results},
language = {eng},
month = {3},
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/194094},
volume = {36},
year = {2010},
}

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
DA - 2010/3//
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.; mixed FEM; numerical results
UR - http://eudml.org/doc/194094
ER -

References

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