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A numerical method for the Cahn-Hilliard equation with a variable mobility. (English) Zbl 1118.35049
Summary: We consider a conservative nonlinear multigrid method for the Cahn-Hilliard equation with a variable mobility of a model for phase separation in a binary mixture. The method uses the standard finite difference approximation in spatial discretization and the Crank-Nicholson semi-implicit scheme in temporal discretization. And the resulting discretized equations are solved by an efficient nonlinear multigrid method. The continuous problem satisfies conservation of mass and decrease of the total energy. It is proved that these properties hold for the discrete problem. Also, we show the proposed scheme has a second-order convergence in space and time numerically. For numerical experiments, we investigate the effects of a variable mobility.
MSC:
35Q72Other PDE from mechanics (MSC2000)
37L65Special approximation methods for infinite-dimensional Hamiltonian systems
65M55Multigrid methods; domain decomposition (IVP of PDE)