  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 is investigated. In
place of solving the original fourth-order system directly, two coupled
second-order systems are solved. The system is solved using an incomplete
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.
