Dual Iterative Techniques for Solving a Finite Element Approximation of the Biharmonic Equation

Ph. Ciarlet; R. Glowinski

Publications mathématiques et informatique de Rennes (1974)

  • Issue: S4, page 1-28

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Ciarlet, Ph., and Glowinski, R.. "Dual Iterative Techniques for Solving a Finite Element Approximation of the Biharmonic Equation." Publications mathématiques et informatique de Rennes (1974): 1-28. <http://eudml.org/doc/273728>.

@article{Ciarlet1974,
author = {Ciarlet, Ph., Glowinski, R.},
journal = {Publications mathématiques et informatique de Rennes},
language = {eng},
number = {S4},
pages = {1-28},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {Dual Iterative Techniques for Solving a Finite Element Approximation of the Biharmonic Equation},
url = {http://eudml.org/doc/273728},
year = {1974},
}

TY - JOUR
AU - Ciarlet, Ph.
AU - Glowinski, R.
TI - Dual Iterative Techniques for Solving a Finite Element Approximation of the Biharmonic Equation
JO - Publications mathématiques et informatique de Rennes
PY - 1974
PB - Département de Mathématiques et Informatique, Université de Rennes
IS - S4
SP - 1
EP - 28
LA - eng
UR - http://eudml.org/doc/273728
ER -

References

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  1. [1] Ciarlet, P.G. ; Raviart, P.-A. : A mixed finite element method for the biharmonic equation. To appear in Proceedings of the Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations, Mathematics Research Center, University of Wisconsin, Madison, April 01-03, 1974. Zbl0337.65058MR657977
  2. [2] Argyris, J.H.; Fried, I. ; Scharpf, D.W. : The TUBA family of plate elements for the matrix displacement method. The Aeronautical J.R.Ae. S.72 (1968), 701-709. 
  3. [3] Ciarlet, P.G. : Conforming and nonconforming finite element methods for solving the plate problem, in Conference on the Numerical Solution of Differential Equations (G.A. Watson, Editor), pp. 21-31, Springer-Verlag, New York, 1974. Zbl0285.65072MR423832
  4. [4] Ciarlet, P.C. : Quelques méthodes d'éléments finis pour le problème d'une plaque encastrée, In Computing Methods In Applied Sciences and Engineering. Part 1 (R. GLOWINSKI and J.L. LIONS, Editors), pp. 156-176, Lecture Notes in Computer Science, Vol. 10, Springer-Verlag, Berlin, 1974. Zbl0285.65042MR440954
  5. [5] Strang, G. : Variational crimes in the finite element method, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, pp. 689-710, Academic Press, New York, 1972. Zbl0264.65068MR413554
  6. [6] 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, in Topics in Numerical Analysis (J.J.H. Miller, Editor), pp. 123-171, Academic Press, London, 1973. Zbl0277.35003MR351120
  7. [7] Oden, J.T. : Some contributions to the mathematical theory of mixed finite element approximations, in Theory and Practice in Finite Element Structural Analysis, pp. 3-23, University of Tokyo Press, 1973. Zbl0374.65060MR309412
  8. [8] Oden, J.T. ; Reddy, J.N. : On dual complementary variational principles in mathematical physics. Int. J. Engng Sci.12 (1974), 1-29. Zbl0273.49066MR451158
  9. [9] Reddy, J.N. : A Mathematical Theory of Complementary-Dual Variational Principles and Mixed Finite-Element Approximations of Linear Boundary-Value Problems in Continuum Mechanics, Ph. D. Dissertation, The University of Alabama in Huntsville, Huntsville, 1973. 
  10. [10] Bossavit, A. : Une méthode de décomposition de l'opérateur biharmonique. Note HI 585/2, Electricité de France, 1971. 
  11. [11] Smith, J. : The coupled equation approach to the numerical solution of the biharmonic equation by finite differences I., SIAM J.Numer, Anal.5 (1968), 323-339. Zbl0165.50801MR233526
  12. [12] Smith, J. : On the approximate solution of the first boundary value problem for 4 u = f , SIAM J. Nuner. Anal.10 (1973), 967-982. Zbl0268.65068MR343665
  13. [13] Ehrlich, L.W. : Solving the biharmonic equation as coupled finite difference equations, SIAM J. Numer. Anal.8 (1971), 278-287. Zbl0215.55702MR288972
  14. [14] McLaurin, J.W. : A general coupled equation approach for solving the biharmonic boundary value problem, SIAM J. Numer. Anal.11 (1974), 14-33. Zbl0237.65067MR349042
  15. [15] Glowinski, R. ; Lions, J.L. ; Tremolieres, R. : Analyse Numérique des Inéquations Variationnelles (to appear). Zbl0358.65091
  16. [16) Ciarlet, P.G. ; Glowinski, R. : Sur la résolution numérique du problème de Dirichlet pour l'opérateur biharmonique. C.R. Acad. Sci.Paris Sér. A (to appear). Zbl0293.65085
  17. [17] Ciarlet, P.G. ; Raviart, P.-A. : La Méthode des Eléments Finis pour les Problèmes aux limites Elliptiques. To appear. 
  18. [18] Necas, J. : Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris, 1967 Zbl1225.35003
  19. [19] Kondrat'Ev, V.A. : Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Mosk. Mat. Obsc.16 (1967), 209-292. Zbl0194.13405MR226187
  20. [20] Ekeland, I.; Temam, R. : Analyse Convexe et Problèmes Variationals. Dunod, Paris, 1974. Zbl0281.49001

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