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The steady, axisymmetric laminar flow of a Newtonian fluid past a centrally-located sphere in a pipe first loses stability with increasing flow rate at a steady, O(2)-symmetry breaking bifurcation point. Using group theoretic results, a number of authors have suggested techniques for locating singularities in branches of solutions which are invariant with… (More)

In this review we discuss bifurcation theory in a Banach space setting using the singularity theory developed by Golubitsky and Schaeffer to classify bi-furcation 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.… (More)

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier–Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady… (More)

Computations of Marangoni convection are usually performed in two-or three-dimensional domains with rigid boundaries. In two dimensions, allowing the free surface to deform can result in a solution set with a qualitatively different bifurca-tion structure. We describe a finite-element technique for calculating bifurcations that arise due to thermal… (More)

2 TAVENER Two immiscible fluid layers that are subjected to a temperature gradient perpendicular to their interface, exhibit a range of behaviors that is considerably richer than for the single-fluid case. We describe a numerical technique for calculating thermally-driven flows in two fluid layers which uses a simple technique based on a Landau… (More)

We present the results of a numerical investigation of the Ericksen-Leslie equations for the problem of electrohydrodynamic convection in a nematic liquid crystal. The combination of a finite element approach and numerical bifurcation techniques allows us to provide details of the basic flow and include the physically relevant effect of nonslip side walls.… (More)

- A D Jepson, A Spencer, K A Cliffe
- 1985

The computation of symmetry-breaking bifurcation points of nonlinear multiparameter problems with Z2 (reflectional) symmetry is considered. The numerical approach is based on recent work in singularity theory, which is used to construct systems of equations and inequalities characterising various types of symmetry-breaking bifurcation points. Numerical… (More)