Optimization in bifurcation problems part I: Theory and illustration

2006 ◽  
pp. 181-190
Author(s):  
J. P. Kernévez ◽  
E. J. Doedel
Keyword(s):  
Bifurcation Problems

GENERALIZED WAVEGUIDE BIFURCATION PROBLEMS

1988 ◽  
Vol 41 (1) ◽  
pp. 127-139 ◽  
Author(s):  
R. A. HURD ◽  
E. MEISTER
Keyword(s):  
Bifurcation Problems

Bifurcation problems in nonlinear parametric programming

1987 ◽  
Vol 39 (2) ◽  
pp. 189-205 ◽  
Author(s):  
A. B. Poore ◽  
C. A. Tiahrt
Keyword(s):  
Parametric Programming ◽  
Bifurcation Problems

Sub- and super-solutions in bifurcation problems

1997 ◽  
Vol 28 (4) ◽  
pp. 625-632 ◽  
Author(s):  
J.L. Gámez
Keyword(s):  
Bifurcation Problems

A solvability of bifurcation problems

2005 ◽  
Vol 63 (5-7) ◽  
pp. e1809-e1816
Author(s):  
In-Sook Kim
Keyword(s):  
Bifurcation Problems

The numerical analysis of bifurcation problems with application to fluid mechanics

Acta Numerica ◽  
2000 ◽  
Vol 9 ◽  
pp. 39-131 ◽  
Author(s):  
K. A. Cliffe ◽  
A. Spence ◽  
S. J. Tavener
Keyword(s):  
Numerical Analysis ◽  
Fluid Mechanics ◽  
Stokes Equations ◽  
Mixed Finite Element ◽  
Finite Difference Methods ◽  
Singularity Theory ◽  
Mixed Finite Element Method ◽  
Convergence Theory ◽  
Navier Stokes ◽  
Bifurcation Problems

In this review we discuss bifurcation theory in a Banach space setting using the singularity theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical analysis of bifurcation problems is discussed and the convergence theory for several important bifurcations is described for both projection and finite difference methods. These results are used to provide a convergence theory for the mixed finite element method applied to the steady incompressible Navier–Stokes equations. Numerical methods for the calculation of several common bifurcations are described and the performance of these methods is illustrated by application to several problems in fluid mechanics. A detailed description of the Taylor–Couette problem is given, and extensive numerical and experimental results are provided for comparison and discussion.

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