Year: 2019
Author: Xiao Li, Lili Ju, Xucheng Meng
Communications in Computational Physics, Vol. 26 (2019), Iss. 5 : pp. 1510–1529
Abstract
In this paper, we rigorously prove the convergence of fully discrete first- and second-order exponential time differencing schemes for solving the Cahn-Hilliard equation. Our analyses mainly follow the standard procedure with the consistency and stability estimates for numerical error functions, while the technique of higher-order consistency analysis is adopted in order to obtain the uniform L∞ boundedness of the numerical solutions under some moderate constraints on the time step and spatial mesh sizes. This paper provides a theoretical support for numerical analysis of exponential time differencing and other related numerical methods for phase field models, in which an assumption on the uniform L∞ boundedness is usually needed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.2019.js60.12
Communications in Computational Physics, Vol. 26 (2019), Iss. 5 : pp. 1510–1529
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Cahn-Hilliard equation exponential time differencing convergence analysis uniform $L^∞$ boundedness.
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