Cahn-Hilliard on surfaces: A numerical study

The Cahn-Hilliard system has been used to describe a wide number of phase separation processes, from co-polymer systems to lipid membranes. In this work the convergence properties of a closest-point based scheme are investigated. In place of solving the original fourth-order system directly, two coupled second-order systems are solved. The system is solved using an approximate Schur-decomposition as a preconditioner. The results indicate that with a sufficiently high-order time discretization the method only depends on the underlying spatial resolution.