An Efficient Two-Grid Scheme for the Cahn-Hilliard Equation. (28th November 2014)

• Record Type: Journal Article
• Authors: Zhou, Jie; Chen, Long; Huang, Yunqing; Wang, Wansheng
• Is Part Of: Communications in computational physics. Volume 17:Number 1(2015:Jan.)
• Page Start: 127
• Page End: 145
• Publication Date: 2014-11-28
• Subjects: 65N30, -- 65N55, -- 68W25; Cahn-Hilliard equation, -- two-grid, -- adaptivity, -- mixed method, -- multigrid; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.231213.100714a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.