Grid design for the computation of a hexagon-roll interaction using a finite element method (Q1360387)

The problem of computing the interaction of hexagon and roll solutions bifurcating from a spatially uniform equilibrium solution of an equivariant partial differential equation is studied. As an example of where such an interaction occurs a partial differential equation describing the directional solidification of a dilute binary alloy is considered. It is shown that if the symmetry is not taken into account, then spurious disconnections can occur. This problem is overcome by constructing novel grids for the finite element method which have hexagonal symmetry and enough translational symmetry to enable the computation of the correct bifurcation structure.