TY - JOUR
T1 - A numerical method for the Cahn-Hilliard equation with a variable mobility
AU - Kim, Junseok
N1 - Funding Information:
The author thanks his advisor, John Lowengrub, for intellectual and financial support. The author acknowledges the support of the National Science Foundation’s Division of Mathematical Sciences. The author also thanks Dr. Hyeong-Gi Lee for very helpful discussions.
PY - 2007/12
Y1 - 2007/12
N2 - 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.
AB - 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.
KW - Cahn-Hilliard equation
KW - Nonlinear multigrid method
KW - Phase separation
KW - Variable mobility
UR - http://www.scopus.com/inward/record.url?scp=34249662156&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34249662156&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2006.02.010
DO - 10.1016/j.cnsns.2006.02.010
M3 - Article
AN - SCOPUS:34249662156
VL - 12
SP - 1560
EP - 1571
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
IS - 8
ER -