期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 200, 期 29-32, 页码 2458-2470出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2011.04.018
关键词
Cahn-Hilliard equation on surface; Finite element approximation; Phase transition; Fully discrete approximation; Pointwise bound; Convergence analysis; Error estimate
资金
- US National Science Foundation [DMS-0913491, DMS-1016073]
In this paper, we consider the phase separation on general surfaces by solving the nonlinear Cahn-Hilliard equation using a finite element method. A fully discrete approximation scheme is introduced, and we establish a priori estimates for the discrete solution that does not rely on any knowledge the exact solution beyond the initial time. This in turn leads to convergence and optimal error estimates of the discretization scheme. Numerical examples are also provided to substantiate the theoretical results. (C) 2011 Elsevier B.V. All rights reserved.
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