Basic compactness properties of nonconforming and hybrid finite element spaces

Friedrich Stummel

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

  • Volume: 14, Issue: 1, page 81-115
  • ISSN: 0764-583X

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Stummel, Friedrich. "Basic compactness properties of nonconforming and hybrid finite element spaces." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 14.1 (1980): 81-115. <http://eudml.org/doc/193353>.

@article{Stummel1980,
author = {Stummel, Friedrich},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonconforming and hybrid finite element spaces; inhomogeneous elliptic variational equations; elliptic eigenvalue problems; Rellich compactness theorem; stability; convergence theorems; perturbation theory for Sobolev spaces},
language = {eng},
number = {1},
pages = {81-115},
publisher = {Dunod},
title = {Basic compactness properties of nonconforming and hybrid finite element spaces},
url = {http://eudml.org/doc/193353},
volume = {14},
year = {1980},
}

TY - JOUR
AU - Stummel, Friedrich
TI - Basic compactness properties of nonconforming and hybrid finite element spaces
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1980
PB - Dunod
VL - 14
IS - 1
SP - 81
EP - 115
LA - eng
KW - nonconforming and hybrid finite element spaces; inhomogeneous elliptic variational equations; elliptic eigenvalue problems; Rellich compactness theorem; stability; convergence theorems; perturbation theory for Sobolev spaces
UR - http://eudml.org/doc/193353
ER -

References

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  4. 4. P. C. CIARLET, The Finite Element Method for Elliptic Problems, North Holland, Amsterdam, 1978. Zbl0383.65058MR520174
  5. 5. M. CROUZEIX and P. A. RAVIART, Conforming and Nonconforming Finite Element Methods for Solving the Stationary Stokes Equations I, R.A.I.R.O., Série Rouge, Anal. Numér., Vol. 3, 1973, pp. 33-76. Zbl0302.65087MR343661
  6. R. D. GRIGORIEFF, Diskrete Approximation von Eigenwertproblemen. I. Qualitative Konvergenz, Numer. Math., Vol. 24, 1974, pp. 355-374; Zbl0391.65020MR423099
  7. II. Konvergenzordnung, Numer. Math., Vol. 24, 1974, pp. 415-433; 
  8. III. Asymptotische Entwicklungen, Numer. Math., Vol. 25, 1975, pp. 79-97. MR423101
  9. 7. B. GRÜNBAUM, Convex Polytopes, Wiley-Interscience, London-New York, 1967. Zbl0163.16603MR226496
  10. 8. P. LASCAUX and P. LESAINT, Some Nonconforming Finite Elements for the Plate Bending Problem, R.A.I.R.O., Série Rouge, Anal. Numér., Vol. 9, 1975, pp. 9-53. Zbl0319.73042MR423968
  11. 9. J. NECAS, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. MR227584
  12. 10. R. RANNACHER, Conconforming Finite Element Methods for Eigenvalue Problems in Linear Plate Theory, Preprint, No. 191, S.F.B. 72, Universität Bonn, 1978. Zbl0394.65035MR784647
  13. 11. P. A. RAVIART and J. M. THOMAS, Primal Hybrid Finite Element Methods for 2nd Order Elliptic Equations, Math. Comp., Vol. 31, 1977, No. 138, pp. 391-413. Zbl0364.65082MR431752
  14. 12. R. T. ROCKAFELLAR, Convex Analysis, University Press, Princeton, 1970. Zbl0193.18401MR274683
  15. 13. F. STUMMEL, Rand-und Eigenwertaufgaben in Sobolewschen Rämen, Lecture Notes in Mathematics, No. 102, Springer-Verlag, Berlin-Heidelberg-New York, 1969. Zbl0177.42402MR463907
  16. 14 F STUMMEL, Diskrete Konvergenz linearer OperatorenI, Math Ann , Vol 190 1970, pp 45-92, II, Math Z , Vol 120, 1971, pp 231-264, III, Proc Conf Linear Operators and Approximation, Oberwolfach, 1971, P L BUTZER, J-P KAHANE and B Sz -NAGY, Eds , Birkhauser Basel, I S N M Vol 20 1972 pp 196-216. Zbl0255.47028
  17. 15 F STUMMEL, Singular Perturbations of Elliptic Sesquilinear Forms, Proc Conf Differential Equations, Dundee, 1972, W N EVERITT and B D SLEEMAN, Eds, Lecture Notes m Mathematics, No 280, 1972, pp 155-180. Zbl0237.35006MR427792
  18. 16 F STUMMEL, Perturbation Theory for Sobolev Spaces, Proc Royal Soc Edmburgh,Vol 73A, 1974/ 1975, pp 1-49. Zbl0358.46027MR410433
  19. 17 F STUMMELPerturbation of Domains in Elliptic Boundary Value Problems, Proc Conf Application of Methods of Functional Analysis to Problems of Mechanics, Marseille, 1975, P GERMAIN and B NAYROLES, Eds , Lecture Notes in Mathematics, No 503, 1976, pp 110-136. Zbl0355.65074MR636392
  20. 18 F STUMMEL, Approximation Methods for Eigenvalue Problems in Elliptic Differential Equations, Proc Conf Numerik und Anwendungen von Eigenwertaufgaben und Verzweigungsproblemen, Oberwolfach 1976 E BOHL L COLLATZ and K P HADFLER Eds Birkhauser Basel I S N M Vol 38 1977 pp 133-165. Zbl0359.65051MR657954
  21. 19 F STUMMELThe Limitations of the Patch Test Int J Numer Meth Eng. Zbl0445.65085
  22. 20 F STUMMELThe Genetalized Patch Test S I A M J Numer Anal Vol 16 1979 pp 449-471. Zbl0418.65058MR530481
  23. 21 J M THOMAS, Sur l'analyse numérique des methodes d'élement finis hybrides et mixtes, These Universite P -et-M-Curie, Pans, 1977. 

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