Conforming equilibrium finite element methods for some elliptic plane problems

Michal Křížek

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1983)

  • Volume: 17, Issue: 1, page 35-65
  • ISSN: 0764-583X

How to cite

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Křížek, Michal. "Conforming equilibrium finite element methods for some elliptic plane problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 17.1 (1983): 35-65. <http://eudml.org/doc/193408>.

@article{Křížek1983,
author = {Křížek, Michal},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {finite element subspaces; spaces of divergence free functions; equilibrium finite element models},
language = {eng},
number = {1},
pages = {35-65},
publisher = {Dunod},
title = {Conforming equilibrium finite element methods for some elliptic plane problems},
url = {http://eudml.org/doc/193408},
volume = {17},
year = {1983},
}

TY - JOUR
AU - Křížek, Michal
TI - Conforming equilibrium finite element methods for some elliptic plane problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1983
PB - Dunod
VL - 17
IS - 1
SP - 35
EP - 65
LA - eng
KW - finite element subspaces; spaces of divergence free functions; equilibrium finite element models
UR - http://eudml.org/doc/193408
ER -

References

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  1. [1] D. J. ALLMAN, On compatible and equilibrium models with linear stresses for stretching of elastic plates, in [27]. Zbl0407.73059
  2. [2] F. BREZZI, Non-standard finite elements for fourth order elliptic problems, in [27]. Zbl0411.41013
  3. [3] G. R. BUSACKER and T. L. SAATY, Finite graphs and network : an introduction with applications, McGraw-Hill, New York, London, Sydney, 1965. Zbl0146.20104MR209176
  4. [4] P. G. CIARLET, The finite element method for elliptic problems, North-Holland publishing company, Amsterdam, NewYork, Oxford, 1978. Zbl0383.65058MR520174
  5. [5] G. DUVAUT and J. L. LIONS, Inequalities in mechanics and physics, Springer-Verlag, Berlin, Heidelberg, NewYork, 1976. Zbl0331.35002MR521262
  6. [6] M. FORTIN, Approximation des fonctions à divergence nulle par la méthode des éléments finis, Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, Paris, 1972, vol. 1, 99-103. Zbl0277.76024MR478666
  7. [7] B. M. FRAEIJS DE VEUBEKE and M. HOGGE, Dual analysis for heat conduction problems by finite elements, Internat. J. Numer. Methods Energ. 5 (1972), 65-82 Zbl0251.65061
  8. [8] V. GIRAULT and P. A. RAVIART, Finite element approximation of the Navier-Stokes equation, Springer-Verlag, Berlin, Heidelberg, New York, 1979. Zbl0413.65081MR548867
  9. [9] R. GLOWINSKI and O. PIRONNEAU, On numerical methods for the Stokes problem, in [27]. Zbl0415.76024
  10. [10] B. J. HARTZ and V. B. WATWOOD, An equilibrium stress field model for finite element solution of two-dimensional electrostatic problems, Internat. J. Solids and Structures 4 (1968), 857-873. Zbl0164.26201
  11. [11] J. HASLINGER and I. HLAVACEK, Convergence of a finite element method based on the dual variational formulation, Apl. Mat. 21 (1976), 43-65. Zbl0326.35020MR398126
  12. [12] I. HLAVACEK, Convergence of an equilibrium finite element model for plane elastostatics, Apl. Mat. 24 (1979), 427-457. Zbl0441.73101MR547046
  13. [13] I. HLAVACEK, The density of solenoidal functions and the convergence of a dual finite element method, Apl. Mat. 25 (1980), 39-55. Zbl0424.65056MR554090
  14. [14] C. JOHNSON, On the convergence of a mixed finite element method for plate bending problems, Numer. Math. 21 (1973), 43-62. Zbl0264.65070MR388807
  15. [15] C. JOHNSON and B. MERCIER, Some equilibrium finite element methods for two-dimensional elasticity problems, Numer. Maht. 30 (1978), 103-116. Zbl0427.73072MR483904
  16. [16] D. W. KELLY, Bounds on discretization error by special reduced integration of the Lagrange family of finite elements, Internat. J. Numer. Methods Energ. 15 (1980), 1489-1506. Zbl0438.73057MR595369
  17. [17] M. KRIZEK, An equilibrium finite element method in three-dimensional elasticity, Apl. Mat. 27 (1982), 46-75. Zbl0488.73072MR640139
  18. [18] B. MERCIER, Topics in finite element solution of elliptic problems, Springer-Verlag, Berlin, Heidelberg, New York, 1979. Zbl0445.65100
  19. [19] J. NECAS, Les méthodes directes en théorie des équations elleptiques, Academia, Prague, 1967. MR227584
  20. [20] J. NECAS and I. HLAVACEK, Mahtematical theory of elastic and elasto-plastic bodies : an introduction, Elsevier Scientific Publishing Company, Amsterdam, Oxford, New York, 1981. Zbl0448.73009MR600655
  21. [21] A. R. S. PONTER, The application of dual minimum theorems to the finite element solution of potential problems with special reference to seepage, Internat. J. Numer. Methods Energ. 4 (1972), 85-93. Zbl0254.76095MR297211
  22. [22] G. SANDER, Application of the dual analysis principle , Proceedings of the IUTAM Symposium on High Speed Computing of Elastic Structures, Congrès et Colloques de l'Université de Liège (1971), 167-207. 
  23. [23] R. TEMAM, Navier-Stokes equations North-Holland publishing company, Amsterdam, New York, Oxford, 1977. Zbl0426.35003MR603444
  24. [24] J. M. THOMAS, Sur l'analyse numérique des méthodes d'éléments finis hybrides et mixtes, Thesis, Université Paris VI, 1977. 
  25. [25] J. M. THOMAS and M. AMARA, Approximation par éléments finis équilibre du système de l'élasticité linéaire, C.R. Acad. Sc. Paris, t. 286 (1978), 1147-1150. Zbl0395.73011MR495556
  26. [26] J. M. THOMAS and M. AMARA, Equilibrium finite elements for the linear elastic problem, Numer. Math. 33 (1979), 367-383. Zbl0401.73079MR553347
  27. [27] Energy methods in finite element analysis, John Wiley & Sons Ltd., Chichester, New York, Brisbane, Toronto, 1979. MR536995

Citations in EuDML Documents

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  1. Michal Křížek, Zdeněk Milka, On an unconventional variational method for solving the problem of linear elasticity with Neumann or periodic boundary conditions
  2. Ivan Hlaváček, Optimization of the domain in elliptic problems by the dual finite element method
  3. Michal Křížek, Pekka Neittaanmäki, Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains
  4. Ivan Hlaváček, Michal Křížek, Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries
  5. Ivan Hlaváček, Michal Křížek, Internal finite element approximation in the dual variational method for the biharmonic problem
  6. Juraj Weisz, A posteriori error estimate of approximate solutions to a mildly nonlinear elliptic boundary value problem
  7. Miroslav Vondrák, Slab analogy in theory and practice of conforming equilibrium stress models for finite element analysis of plane elastostatics

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