Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 12, Issue 8, Pages 1560-1571Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2006.02.010
Keywords
Cahn-Hilliard equation; Variable mobility; Nonlinear multigrid method; Phase separation
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Funding
- National Science Foundation's Division of Mathematical Sciences
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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 has the conservation of mass and the 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. (C) 2006 Elsevier B. V. All rights reserved.
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