The Use of Symmetry in Bifurcation Calculations and Its Application to the Béenard Problem
Abstract
Some aspects of the use of symmetry in bifurcation calculations are discussed. First, it is shown how substantial reductions in cost are obtained in computing symmetrybreaking bifurcation points by exploiting the underlying symmetry of a problem. This is demonstrated in a finiteelement calculation of 2dimensional Benard convection in a finite cavity. Second, the stability of paths of symmetrybreaking bifurcation points, which occur when a second parameter in the problem varies, is investigated. A criterion is established for deciding whether intersection of such paths is allowed by symmetry constraints.
 Publication:

Journal of Computational Physics
 Pub Date:
 December 1986
 DOI:
 10.1016/00219991(86)902652
 Bibcode:
 1986JCoPh..67..310C
 Keywords:

 Branching (Mathematics);
 Broken Symmetry;
 RayleighBenard Convection;
 Finite Element Method;
 Perturbation Theory;
 Rayleigh Number;
 Fluid Mechanics and Heat Transfer