A numerical method for the ternary Cahn-Hilliard system with a degenerate mobility (Q1012248)

The purpose of this paper is to consider the conservative nonlinear multigrid method for the ternary Cahn-Hilliard (CH) system with a concentration dependent degenerate mobility for a three component mixture. First, a fully discrete semi-implicit finite difference scheme is considered. Assuming that the nonlinear system at an implicit time step is solvable, the authors establish the mass conservation and prove that the energy functional is nonincreasing in time, provided that the step size of time is sufficiently small. Then, a nonlinear multigrid V-cycle algorithm for the ternary CH system is also described. Numerical experiments such as a second-order convergence test, comparison with linear stability analysis, different boundary conditions and effects of a concentration dependent mobility are presented.