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

Bhattacharyya, Pulin Kumar; Nataraj, Neela

doi:10.1051/m2an:2002001

Bhattacharyya, Pulin Kumar ; Nataraj, Neela

ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 1, pp. 1-32.

Résumé

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 $Ψ = {(ψ_{i j})}_{1 \leq i, j \leq 2}$ and displacement field ‘u’, have been developed.

MR Zbl

DOI : 10.1051/m2an:2002001

Classification : 35J40, 65N30, 35P99, 74H45
Mots clés : mixed FEM, eigenvalue problem, isoparametric boundary approximation, 4th-order equations, anisotropic plates, convergence analysis, numerical results

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     title = {Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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     publisher = {EDP-Sciences},
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     number = {1},
     year = {2002},
     doi = {10.1051/m2an:2002001},
     mrnumber = {1916290},
     zbl = {0993.35031},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an:2002001/}
}

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Bhattacharyya, Pulin Kumar; Nataraj, Neela. Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 1, pp. 1-32. doi : 10.1051/m2an:2002001. http://www.numdam.org/articles/10.1051/m2an:2002001/

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