×

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
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ciarlet, P. G.; Raviart, P. A., A mixed finite element method for the biharmonic equation, (de Boor, C., Proc. Symp. on Mathematical Aspects of Finite Elements in Partial Differential Equations (1974), Acad. Press: Acad. Press N.Y), 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, (Miller, J. H.H., Topics in numerical analysis (1973), Academic Press: Academic Press London), 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: 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.; 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: Prentice-Hall Englewood Cliffs, New Jersey · Zbl 0133.08602
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.