COMPARISON OF DIFFERENT NUMERICAL SCHEMES FOR THE CAHN-HILLIARD EQUATION

In this work, we numerically analyze a class of time discretizations for the Cahn-Hilliard equation. It is useful to investigate the performance of different schemes in terms of accuracy and efficiency since these schemes are frequently used in various science applications. In this work, comparisons of the explicit Euler’s, implicit Euler’s, Crank-Nicolson, semi-implicit Euler’s, linearly stabilized splitting, and non-linearly stabilized splitting schemes are presented. The continuous problem has the conservation of mass and the decrease of the total energy. We check the same properties hold for the discrete problem.