Parameter-Free Time Adaptivity Based on Energy Evolution for the Cahn-Hilliard Equation. (17th May 2016)

• Record Type: Journal Article
• Authors: Luo, Fuesheng; Tang, Tao; Xie, Hehu
• Is Part Of: Communications in computational physics. Volume 19:Number 5(2016:May)
• Page Start: 1542
• Page End: 1563
• Publication Date: 2016-05-17
• Subjects: 65N10, -- 65N15, -- 35J25, -- 35Q99, -- 35R99, -- 65M12, -- 65M70; Adaptive time-stepping method, -- Cahn-Hilliard equation, -- Crank-Nicolson scheme, -- convex splitting method; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.scpde14.45s
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: It is known that large time-stepping method are useful for simulating phase field models. In this work, an adaptive time-stepping strategy is proposed based on numerical energy stability and equi-distribution principle. The main idea is to use the energy variation as an indicator to update the time step, so that the resulting algorithm is free of user-defined parameters, which is different from several existing approaches. Some numerical experiments are presented to illustrate the effectiveness of the algorithms.