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An Efficient Two-Grid Scheme for the Cahn-Hilliard Equation

Published online by Cambridge University Press:  28 November 2014

Jie Zhou ,
Long Chen ,
Yunqing Huang  and
Wansheng Wang
Jie Zhou
Affiliation:
School of Mathematics and, Computational Science in Xiangtan University, Xiangtan 411105, China
Long Chen*
Affiliation:
Department of Mathematics, University of California, Irvine, CA 92697-3875, USA
Yunqing Huang
Affiliation:
School of Mathematics and, Computational Science in Xiangtan University, Xiangtan 411105, China Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, Xiangtan University, Hunan 411105, China
Wansheng Wang
Affiliation:
School of Mathematics and Computational Science, Changsha University of Science & Technology, Yuntang Campus, 410114 Changsha, China
*
*Email addresses:xnuzj2004@163.com(J. Zhou), chenlong@math.uci.edu(L. Chen), Huangyq@xtu.edu.cn(Y. Huang), w.s.wang@163.com(W.Wang)
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Abstract

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.

Keywords

65N3065N5568W25Cahn-Hilliard equationtwo-gridadaptivitymixed methodmultigrid
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 1 , January 2015 , pp. 127 - 145
Copyright
Copyright © Global Science Press Limited 2015 

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