Skip to main content

Finite element approximations to bifurcation problems of turning point type

Non-Linear Problems, Bifurcation

Part of the Lecture Notes in Mathematics book series (LNM,volume 704)

Keywords

  • Finite Element Method
  • Implicit Function Theorem
  • Zero Eigenvalue
  • Finite Element Approximation
  • Bifurcation Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Weiss: Bifurcation in difference approximation to two-point boundary value problems, Math. Comp. 29 (1975) 746–760.

    CrossRef  MATH  Google Scholar 

  2. F. Kikuchi: An iterative finite element scheme for bifurcation analysis of semi-linear elliptic equations, ISAS Report, University of Tokyo, No. 542 (1976) 203–231.

    Google Scholar 

  3. M. Yamaguchi and H. Fujii: On numerical deformations of singularities in nonlinear elasticity, this Symposium (1977).

    Google Scholar 

  4. C. Bolley: Etude numérique d'un problème de bifurcation, Thesis, Universite de Rennes (1977).

    Google Scholar 

  5. A. Mizutani: On the finite element method for Δu + μu − f(x,u) = 0, to appear.

    Google Scholar 

  6. R. B. Simpson: Existence and error estimates for solutions of a discrete analog of nonlinear eigenvalue problems, Math. Comp. 26 (1972) 190–211.

    CrossRef  MathSciNet  Google Scholar 

  7. R. B. Simpson: A method for the numerical determination of bifurcation states of nonlinear systems of equations, SIAM J. Numer. Anal. 12 (1975) 439–451.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. H. B. Keller: Nonlinear bifurcation, J. Diff. Eq. 7 (1970) 417–434.

    CrossRef  MATH  Google Scholar 

  9. J. B. Keller and S. Antman (editors): Bifurcation Theory and Nonlinear Eigenvalue Problems, Benjamin (1969).

    Google Scholar 

  10. M. A. Krasnosel'skii et al.: Approximate Solutions of Operator Equations, Wolters-Noordhoff (1972).

    Google Scholar 

  11. D. H. Sattinger: Topics in Stability and Bifurcation Theory, Lecture Notes in Mathematics, #309, Springer (1973).

    Google Scholar 

  12. L. Nirenberg: Topics in Nonlinear Functional Analysis, Courant Institute of Mathematical Sciences, New York University (1974).

    Google Scholar 

  13. H. B. Keller and A. W. Wolfe: On the non-unique equilibrium states and buckling mechanism of spherical shells, SIAM J. 13 (1965) 674–705.

    MathSciNet  MATH  Google Scholar 

  14. P. Grisvard: Behavior of the solutions of an elliptic boundary value problem in a polygonal or polyhedral domain, in Numerical Solution of Partial Differential Equations-III, SYNSPADE 1975, edited by B. Hubbard, Academic Press (1976) 204–274.

    Google Scholar 

  15. G. Strang and G. J. Fix: An Analysis of the Finite Element Method, Prentice-Hall (1973).

    Google Scholar 

  16. F. Kikuchi: Numerical analysis of the finite element method applied to bifurcation problems of turning point type, to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1979 Springer-Verlag

About this paper

Cite this paper

Kikuchi, F. (1979). Finite element approximations to bifurcation problems of turning point type. In: Glowinski, R., Lions, J.L., Laboria, I. (eds) Computing Methods in Applied Sciences and Engineering, 1977, I. Lecture Notes in Mathematics, vol 704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063624

Download citation

  • DOI: https://doi.org/10.1007/BFb0063624

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09123-3

  • Online ISBN: 978-3-540-35411-6

  • eBook Packages: Springer Book Archive