The Fourier Spectral Method For A Class Of Cahn-Hilliard Equations

Nonlinear parabolic equation appears in many practical areas, it can be used to describe the groundwater flow, air flow, controlled nuclear fusion and other physical system that in-cluding mass diffusion and energy transfer process. Numerical simulation of the actual phys-ical processes is a cutting-edge research in computing science and engineering fields, and the study of discrete method for atypical parabolic equations has always been a challenging task.This paper discusses a class of Cahn-Hilliard equations: whereWe introduced the background and theoretical knowledge of the class of Cahn-Hilliard equations. Firstly, we derived the semi-discrete scheme by an equivalent variational equa-tions and obtained the H0,H1,H2 norm stabilities of the semi-discrete solutions; Then,we used the orthogonal projection operator to split the error, and analyzed the nonlinear terms respectively and we obtained the error estimates of semi-discrete solution; Finally, a half implicit full-discrete scheme is given which lead to a linear equation.Then, we analysed the H0,H1 norm priori estimates of the full-discrete solutions and the error estimate of full-discrete solution.