An efficient two-grid method for the Cahn–Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential

摘要

In this paper, we consider the two-grid method for solving Cahn–Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential. This two-grid method consists of two steps. First step, solve the Cahn–Hilliard equation with full implicit mixed finite element method and Newton iteration method on a coarse grid. Second step, solve two linear equations on a fine grid. The stability and convergence of the proposed scheme are established. Finally, some numerical experiments are presented.