Effective time step analysis of a nonlinear convex splitting scheme for the Cahn–Hilliard equation

We analyze the effective time step size of a nonlinear convex splitting scheme for the Cahn–Hilliard (CH) equation. The convex splitting scheme is unconditionally stable, which implies we can use arbitrary large time-steps and get stable numerical solutions. However, if we use a too large time-step, then we have not only discretization error but also time-step rescaling problem. In this paper, we show the time-step rescaling problem from the convex splitting scheme by comparing with a fully implicit scheme for the CH equation. We perform various test problems. The computation results confirm the time-step rescaling problem and suggest that we need to use small enough time-step sizes for the accurate computational results.