Simulating Phase Transition Dynamics on Non-trivial Domains

Abstract

Our goal is to investigate the influence of the geometry and topology of the domain Ω on the solutions of the phase transition and other diffusion-driven phenomena in Ω, modeled e.g. by the Allen-Cahn, Cahn-Hilliard, reaction--diffusion equations. We present FEM numerical schemes for the Allen--Cahn and Cahn--Hilliard equation based on the Eyre's algorithm and present some numerical results on split and dumbbell domains.