Effective Time Step Analysis of a Nonlinear Convex Splitting Scheme for the Cahn–Hilliard Equation (Communications in Computational Physics, 2018)
We analyze the effective time step size of a nonlinear convex splitting schemefor the Cahn–Hilliard (CH) equation. The convex splitting scheme is unconditionallystable, which implies we can use arbitrary large time-steps and get stable numericalsolutions. However, if we use a too large time-step, then we have not only discretizationerror but also time-step rescaling problem. In this paper, we show the time-steprescaling problem from the convex splitting scheme by comparing with a fully implicitscheme for the CH equation. We perform various test problems. The computation resultsconfirm the time-step rescaling problem and suggest that we need to use smallenough time-step sizes for the accurate computational results.