On nonconforming an mixed finite element methods for plate bending problems. The linear case

Rolf Rannacher

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1979)

  • Volume: 13, Issue: 4, page 369-387
  • ISSN: 0764-583X

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Rannacher, Rolf. "On nonconforming an mixed finite element methods for plate bending problems. The linear case." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 13.4 (1979): 369-387. <http://eudml.org/doc/193348>.

@article{Rannacher1979,
author = {Rannacher, Rolf},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {numerical solution; fourth order elliptic boundary value problem; finite element method; displacement method; error estimates},
language = {eng},
number = {4},
pages = {369-387},
publisher = {Dunod},
title = {On nonconforming an mixed finite element methods for plate bending problems. The linear case},
url = {http://eudml.org/doc/193348},
volume = {13},
year = {1979},
}

TY - JOUR
AU - Rannacher, Rolf
TI - On nonconforming an mixed finite element methods for plate bending problems. The linear case
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1979
PB - Dunod
VL - 13
IS - 4
SP - 369
EP - 387
LA - eng
KW - numerical solution; fourth order elliptic boundary value problem; finite element method; displacement method; error estimates
UR - http://eudml.org/doc/193348
ER -

References

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  1. 1. F. BREZZI and P. A. RAVIART, Mixed Finite Element Methodsfor 4th Order Ellipticquations In Topics inNumerical Analysis, Vol.III, J. J. H. MILLER, Ed., Academic Press, 1978. Zbl0434.65085
  2. 2. P. G. CIARLET, Conforming and Nonconforming Finite Element Methods for SolvingthePlate ProblemIn Numerical Solution of Differential Equations, G. A.WATSON, Ed., Springer, 1974. Zbl0285.65072MR423832
  3. 3. P.G. CIARLET and P.A. RAVIART, A mixed Finite Element Method for the Biharmonic Equation In Mathematical Aspects of Finite Eléments in Partial Differential Equations, C. DEBOOR, Ed., Academic Press, 1974. Zbl0337.65058
  4. 4. P. LASCAUX and P. LESAINT, Some Nonconforming Finite Elements for the Plate Bending Problem, R.A.I.R.O., Anal. Nurnér., Vol. 1, 1975, pp. 9-53 Zbl0319.73042MR423968
  5. 5. T. MIYOSHI, Finite Element Method for the Solution of A-th Order Partial Differential Equations, Kumamoto J. Sc.Math., Vol. 9, 1973, pp. 87-116. Zbl0249.35007MR386298
  6. 6. J. A. NITSCHE, Convergence of Nonconforming Methods In Numerical Solution of Differential Equations, G. A. WATSON, Ed., Springer, 1974. Zbl0367.65064MR658316
  7. 7. J. A.N NITSCHE, On Projection Methods for the Plate Problem In Numerical Analysis, J. DESCLOUX and J. MARTI, Ed., Birkhauser, 1977. Zbl0361.65097MR468521
  8. 8. R. RANNACHER, Punktweise Konvergenz der Methode der finiten Elemente beimPlattenproblem, Manuscripta math., Vol. 19, 1976, pp. 401-416. Zbl0383.65061MR423841
  9. 9. R. RANNACHER, Finite Element Approximation of Simply Supported Plates and the Babuska Paradox, Z. Angew. Math. Mech., Vol. 59, 1979, pp. T 73-T 76 Zbl0421.73072MR533989
  10. 10. R RANNACHER, Nonconforming Finite Element Methods for Eigenvalue Problems in Linear Plate Theory, Numer. Math., Vol. 32, 1979 (to appear). Zbl0394.65035MR545740
  11. 11. R. SCHOLZ, Approximation von Sattelpunkten mit finiten Elementen In Finite Elemente,Tagungsband, Bonn, Math. Schr., Vol. 89, 1976, pp. 53-66. Zbl0359.65096MR471377
  12. 12. R. SCHOLZ, A Mixed Methodfor 4th Order Problems using Linear Finite Eléments, R.A.I.R.O., Anal. Numer., Vol. 12, 1978, pp. 85-90. Zbl0382.65059MR483557
  13. 13. J. FREHSE and R. RANNACHER, Eine L 1 -Fehlerabschätzung für diskrete Grundlösungen in der Methode der finiten Elemente In Finite Elemente,Tagungsband, Bonn, Math.Schr., Vol. 89, 1976, pp. 92-114. Zbl0359.65093MR471370
  14. 14. J. A. NITSCHE, L -convergence of finite element approximations, Second Conference on Finite Eléments, Rennes, 1975. Zbl0362.65088MR568857
  15. 15. R. SCOTTOptimal L estimates for the finite element method on irregular meshes, Math. Comp., Vol. 30, 1976, pp. 681-697. Zbl0349.65060MR436617
  16. 16. R. B. KELLOGG and J. E. OSBORN, A Regularity Resuit for the Stokes Problem in aConvex Poligon. J. Funet. Anal., Vol. 21, 1976, pp.397-431. Zbl0317.35037MR404849

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