FOURIER COLLOCATION AND FOURIER GALERKIN METHODS APPLIED TO THE PHASE-FIELD MODEL OF 2-DIMENSIONAL PHASE-TRANSITION PROBLEMS

Fourier collocation and Fourier Galerkin methods were employed for num erical solution of phase-transition problems in two dimensions using t he phase-field model. These methods were chosen in order to be able to describe naturally the temporal evolution of periodic structures. The applications to a modified Stefan problem and interphase boundary mot ion driven by mean curvature are discussed. These two particular probl ems were chosen because their phase-field description has received muc h attention both from mathematical and from computational points of vi ew. These phase-transition problems were modelled in a two-dimensional periodic cell with no boundary conditions applied explicitly to the g overning equations. This procedure allows modelling of more complicate d periodic structures than those described here.