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Numerical study of a dual iterative method for solving a finite element approximation of the biharmonic equation. (English) Zbl 0335.65052


MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J35 Variational methods for higher-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
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[1] Ciarlet, P.G.; Raviart, P.A., A mixed finite element method for the biharmonic equation, (), 125-145 · Zbl 0337.65058
[2] Glowinski, R., Approximations externes, par éléments finis de Lagrange d’ordre un et deux, du problème de Dirichlet pour l’opérateur biharmonique. Méthodes itératives de résolution des problèmes approchés, (), 123-171 · Zbl 0277.35003
[3] Ciarlet, P.G.; Glowinski, R., Dual iterative techniques for solving a finite element approximation of the biharmonic equation, Comp. meths. appl. mech. eng., 5, 277-295, (1975) · Zbl 0305.65068
[4] Argyris, J.H.; Fried, I.; Scharpf, D.W., The TUBA family of plate elements for the matrix displacement method, Aero. J. aero. sci., 72, 701-709, (1968)
[5] Smith, J., The coupled equation approach to the numerical solution of the biharmonic equation by finite differences. I, SIAM J. numer. anal., 5, 323-339, (1968) · Zbl 0165.50801
[6] Glowinski, R.; Lions, J.L.; Tremolieres, R., Analyse numérique des inéquations variationnelles, (1976), Dunod Paris · Zbl 0358.65091
[7] B. Mercier, On the frontal method for finite elements and associated questions of re-ordering. To be published in Rapport Laboria.
[8] Varga, R.S., Matrix iterative analysis, (1962), Prentice-Hall Englewood Cliffs, New Jersey · Zbl 0133.08602
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