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In this paper, we rigorously prove the convergence of fully discrete firstand second-order exponential time differencing schemes for solving the Cahn-Hilliard equation. Our analyses mainly follow the standard procedure with… Click to show full abstract
In this paper, we rigorously prove the convergence of fully discrete firstand 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. AMS subject classifications: 35K55, 65M12, 65M15, 65F30
Journal Title: Communications in Computational Physics
Year Published: 2019
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