摘要
A two-grid method for solving the Cahn-Hilliard equation is proposed in this paper.This two-grid method consists of two steps.First,solve the Cahn-Hilliard equation with an implicit mixed finite element method on a coarse grid.Second,solve two Poisson equations using multigrid methods on a fine grid.This two-grid method can also be combined with local mesh refinement to further improve the efficiency.Numerical results including two and three dimensional cases with linear or quadratic elements show that this two-grid method can speed up the existing mixed finite method while keeping the same convergence rate.
基金
The research of J.Zhou was supported by Graduate innovation program of Hunan province in China(Grant No.CX2012B240)
China Scholarship Council and Natural Science Foundation of China(Grant No.11201159)
L.Chen was supported by NSF Grant DMS-1115961,and in part by Department of Energy prime award#DE-SC0006903
The research of Y.Q.Huang was partially supported by the National Natural Science Foundation of China(Grant No.91430213)
Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1179)
International Science and Technology Cooperation Program of China(Grant No.2010DFR00700)
The research of W.S.Wang was supported by Ky and Yu-Fen Fan Fund Travel Grant from the AMS,the National Natural Science Foundation of China(Grant No.11001033,11371074)
the Natural Science Foundation for Distinguished Young scholars in Hunan Province,China(Grant No.13JJ1020)
the Research Foundation of Education Bureau of Hunan Province,China(Grant No.13A108).
