Error Estimation of a Class of Stable Spectral Approximation to the Cahn-Hilliard Equation

In this work, the initial-boundary value problem of two-dimensional Cahn-Hilliard equation is considered. A class of fully discrete dissipative Fourier spectral schemes are proposed. The existence of the numerical solution is proved by a series of a priori estimations and the Brower fixed point theorem. The uniqueness of the numerical solution is discussed. The optimal converge rate is obtained by the energy method. The numerical simulations are performed to demonstrate the effectiveness of the proposed schemes.