On the stabilization size of semi-implicit Fourier-spectral methods for 3D Cahn–Hilliard equations

Abstract

The stabilized semi-implicit time-stepping method is an efficient algorithm to simulate phased field problems with fourth order dissipation. We consider the 3D Cahn–Hilliard equation and prove unconditional energy stability of the corresponding stabilized semi-implicit Fourier spectral scheme independent of the time step. We do not impose any Lipschitz-type assumption on the nonlinearity. It is shown that the size of the stabilization term depends only on the initial data and the diffusion coefficient. Unconditional Sobolev bounds of the numerical solution are obtained and the corresponding error analysis under nearly optimal regularity assumptions is established.