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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. Weiss: Bifurcation in difference approximation to two-point boundary value problems, Math. Comp. 29 (1975) 746–760.
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.
M. Yamaguchi and H. Fujii: On numerical deformations of singularities in nonlinear elasticity, this Symposium (1977).
C. Bolley: Etude numérique d'un problème de bifurcation, Thesis, Universite de Rennes (1977).
A. Mizutani: On the finite element method for Δu + μu − f(x,u) = 0, to appear.
R. B. Simpson: Existence and error estimates for solutions of a discrete analog of nonlinear eigenvalue problems, Math. Comp. 26 (1972) 190–211.
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.
H. B. Keller: Nonlinear bifurcation, J. Diff. Eq. 7 (1970) 417–434.
J. B. Keller and S. Antman (editors): Bifurcation Theory and Nonlinear Eigenvalue Problems, Benjamin (1969).
M. A. Krasnosel'skii et al.: Approximate Solutions of Operator Equations, Wolters-Noordhoff (1972).
D. H. Sattinger: Topics in Stability and Bifurcation Theory, Lecture Notes in Mathematics, #309, Springer (1973).
L. Nirenberg: Topics in Nonlinear Functional Analysis, Courant Institute of Mathematical Sciences, New York University (1974).
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.
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.
G. Strang and G. J. Fix: An Analysis of the Finite Element Method, Prentice-Hall (1973).
F. Kikuchi: Numerical analysis of the finite element method applied to bifurcation problems of turning point type, to appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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
