期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 388, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.cam.2020.113300
关键词
Cahn-Hilliard equation; Uniform-in-time H-m0 stability; Linearized spectrum estimate; Error analysis with an improved convergence constant
资金
- National Science Foundation (NSF), United States [DMS-2012669]
- NSF, United States [DMS-1719854, DMS-2012634]
- National Science Foundation of China (NSFC) [11971342]
In this paper, an error analysis for a second order accurate numerical scheme for the 2-D and 3-D Cahn-Hilliard equation is presented, with an improved convergence constant that depends on 1/epsilon only in a polynomial order. The study overcomes a well-known difficulty by applying a spectrum estimate for the linearized Cahn-Hilliard operator and performing a detailed numerical analysis.
In this paper we present an error analysis for a second order accurate numerical scheme for the 2-D and 3-D Cahn-Hilliard (CH) equation, with an improved convergence constant. The unique solvability, unconditional energy stability, and a uniform-in-time H-2 stability of this numerical scheme have already been established. However, a standard error estimate gives a convergence constant in an order of exp(CT epsilon(-m0)), with m(0) a positive integer and the interface width parameter epsilon being small, which comes from the application of discrete Gronwall inequality. To overcome this well-known difficulty, we apply a spectrum estimate for the linearized Cahn-Hilliard operator (Alikakos and Fusco, 1993; Chen, 1994; Feng and Prohl, 2004), perform a detailed numerical analysis, and get an improved estimate, in which the convergence constant depends on 1/epsilon only in a polynomial order, instead of the exponential order. (C) 2020 Elsevier B.V. All rights reserved.
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