The Fourier spectral method for the Cahn-Hilliard equation (Q814725)

This paper is concerned with a Fourier spectral method for the numerical solution of the 1D Cahn-Hilliard equation with periodic boundary condition. The authors propose a semi-discrete and a fully discrete schemes that preserve the energy dissipation and mass conservation from the corresponding continuous problem. Moreover, existence and uniqueness of numerical solutions are proved and optimal error bounds are obtained. Numerical tests are presented which demonstrate the schemes.