Commun. Comput. Phys.,
Mesh Sensitivity for Numerical Solutions of Phase-Field Equations Using r-Adaptive Finite Element Methods
Heyu Wang 1*, Ruo Li 21 College of Computer Science, Zhejiang University, Hangzhou 310027, China; and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
2 LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China.
Received 18 January 2007; Accepted (in revised version) 25 May 2007
Available online 27 September 2007
There have been several recent papers on developing moving mesh methods for solving phase-field equations. However, it is observed that some of these moving mesh solutions are essentially different from the solutions on very fine fixed meshes. One of the purposes of this paper is to understand the reason for the differences. We carried out numerical sensitivity studies systematically in this paper and it can be concluded that for the phase-field equations, the numerical solutions are very sensitive to the starting mesh and the monitor function. As a separate issue, an efficient alternating Crank-Nicolson time discretization scheme is developed for solving the nonlinear system resulting from a finite element approximation to the phase-field equations.AMS subject classifications: 65M20, 65M50, 65M60, 80A22
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Key words: Phase-field equations, moving mesh method, Crank-Nicolson scheme, numerical sensitivity.
Email: firstname.lastname@example.org (H. Wang), email@example.com (R. Li)