An unconditionally energy-stable second-order time-accurate scheme for the Cahn-Hilliard equation on surfaces

In this paper, we propose an unconditionally energy-stable second-order time-accurate scheme for the Cahn-Hilliard equation on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. The proposed scheme, which combines a Crank-Nicolson-type scheme with a linearly stabilized splitting scheme, is second-order accurate in time. The discrete system is shown to be conservative and unconditionally energy-stable. The resulting system of discrete equations is simple to implement, and can be solved using a biconjugate gradient stabilized method. We demonstrate the performance of our proposed algorithm through several numerical experiments.