A mixed finite element method for the biharmonic problem

T. Scapolla

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1980)

  • Volume: 14, Issue: 1, page 55-79
  • ISSN: 0764-583X

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Scapolla, T.. "A mixed finite element method for the biharmonic problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 14.1 (1980): 55-79. <http://eudml.org/doc/193352>.

@article{Scapolla1980,
author = {Scapolla, T.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mixed finite element method; biharmonic problem; approximation scheme of higher order; plate deflections},
language = {eng},
number = {1},
pages = {55-79},
publisher = {Dunod},
title = {A mixed finite element method for the biharmonic problem},
url = {http://eudml.org/doc/193352},
volume = {14},
year = {1980},
}

TY - JOUR
AU - Scapolla, T.
TI - A mixed finite element method for the biharmonic problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1980
PB - Dunod
VL - 14
IS - 1
SP - 55
EP - 79
LA - eng
KW - mixed finite element method; biharmonic problem; approximation scheme of higher order; plate deflections
UR - http://eudml.org/doc/193352
ER -

References

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  2. 2. F. BREZZI, On the Existence Uniqueness and Approximation of Saddle-Point Problems Arising from Lagrangian Multipliers, R.A.I.R.O., Vol. 8, R 2, 1974, pp. 129-151 Zbl0338.90047MR365287
  3. 3. F. BREZZI and L. D. MARINI, On the Numerical Solution of Plate Bending Problems by Hybrid Mathods, R.A.I.R.O., Vol. 9, R 3, 1975, pp.5-50. Zbl0322.73048
  4. 4 F BREZZI and P A RAVIART, Mixed Finite Element Methods for 4th Order Elliptic Equations, Proc of the Royal Insh Academy Conference on Numencal Analysis, 1976, Academic Press, London, 1977 Zbl0434.65085MR657975
  5. 5 J CEA, Approximation variationnelle des problèmes aux limites, Ann Inst Fourier,Vol 14, 1964, pp 345-444 Zbl0127.08003MR174846
  6. 6 P G CIARLET, Quelques méthodes d'éléments finis pour le problème d'une plaque encastrée, Colloque I R I A sur « Méthodes de calcul scientifique et technique », Roquencourt, Pans, 17-21 décembre 1973, Springer-Verlag, Berlin, 1974 Zbl0285.65042MR440954
  7. 7 P G CIARLET, The Finite Element Method for Elliptic Problems, North Holland Publishing Co Amsterdam 1978 Zbl0383.65058MR520174
  8. 8 P G CIARLET and P A RAVIART, General Lagrange and Hermite Interpolation in R n with Applications to Finite Element Methods, Arch Rath Mech Anal, Vol 46, 1972, pp 177-199 Zbl0243.41004MR336957
  9. 9 P G CIARLET and P A RAVIART, A Mixed Finite Element Method for the Biharmonic Equation, Symposium on Mathematical Aspects of Finite Elements m Partial Differential Equations, C DE BOOR, Éd , Academic Press, New York, 1974, pp 125-145 Zbl0337.65058MR657977
  10. 10 G FICHERA, Linear Elliptic Differential Systems and Eigenvalue Problems, Lectur Notes, Springer-Verlag, Berlin, 1965 Zbl0138.36104MR209639
  11. 11 M FORTIN, An Analysis of the Convergence of Mixed Finite Element Methods, R A I R O , Numer Anal, Vol 11, No 4, 1977, pp 341-354 Zbl0373.65055MR464543
  12. 12 C JOHNSON, On the Convergence of a Mixed Finite Element Method for Plate Bending Problems, Numer Math , Vol 21, 1973, pp 43-62 Zbl0264.65070MR388807
  13. 13 C JOHNSON, Convergence of Another Mixed Finite Element Method for Plate Bending Problems, Report No 27, Department of Mathematics, Chalmers Institute of Technology and the University of Goteborg, 1972 
  14. 14 J L LIONS and E MAGENES, Problèmes aux limites non homogènes et applications, Vol 1, Travaux Recherches Math , No 17, Dunod, Pans, 1968 Zbl0165.10801MR247243
  15. 15 T MJYOSHI, Finite Element Method for the Solution of Fourth Order Partial Differential Equations, Kunamoto J Sc Math , Vol 9, 1973, pp 87-116 
  16. 16 P A RAVIART, Méthode des éléments finis, Cours 1972-1973 à l'Université de Pans VI 
  17. 17 R SCHOLZ, A Mixed Method for 4th Order Problems Using Linear Finite Elements, R A I R O , Numer Anal , Vol 12, No 1, 1978, pp 85-90 Zbl0382.65059MR483557
  18. 18 G STRANG and G Fix, An Analysis of the Finite Element Method, Prentice Hall Englewood Cliffs, 1973 Zbl0356.65096MR443377
  19. 19 S TIMOSCHENKO, Theory of Plates and Shells, McGraw-Hill, New York, 1959 JFM66.1049.02

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