A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation
暂无分享,去创建一个
The Cahn-Hilliard equation is a nonlinear evolutionary equation that is of fourth order in space. In this paper a linearized finite difference scheme is derived by the method of reduction of order. It is proved that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. The coefficient matrix of the difference system is symmetric and positive definite, so many well-known iterative methods (e.g. Gauss-Seidel, SOR) can be used to solve the system.
[1] C. M. Elliott,et al. Numerical Studies of the Cahn-Hilliard Equation for Phase Separation , 1987 .
[2] Charles M. Elliott,et al. Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation , 1992 .
[3] C. M. Elliott,et al. A nonconforming finite-element method for the two-dimensional Cahn-Hilliard equation , 1989 .
[4] L. Segel,et al. Nonlinear aspects of the Cahn-Hilliard equation , 1984 .