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, Volume 36 (2002) no. 1, p. 1-32
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 ij ) 1i,j2 and displacement field ‘u’, have been developed.
DOI : https://doi.org/10.1051/m2an:2002001
Classification:  35J40,  65N30,  35P99,  74H45
Keywords: mixed FEM, eigenvalue problem, isoparametric boundary approximation, 4th-order equations, anisotropic plates, convergence analysis, numerical results
@article{M2AN_2002__36_1_1_0,
     author = {Bhattacharyya, Pulin Kumar and Nataraj, Neela},
     title = {Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {1},
     year = {2002},
     pages = {1-32},
     doi = {10.1051/m2an:2002001},
     zbl = {0993.35031},
     mrnumber = {1916290},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2002__36_1_1_0}
}
Bhattacharyya, Pulin Kumar; 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, Volume 36 (2002) no. 1, pp. 1-32. doi : 10.1051/m2an:2002001. http://www.numdam.org/item/M2AN_2002__36_1_1_0/

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