Volume 26, Issue 5
Convergence Analysis of Exponential Time Differencing Schemes for the Cahn-Hilliard Equation

Xiao Li ,  Lili Ju and Xucheng Meng

10.4208/cicp.2019.js60.12

Commun. Comput. Phys., 26 (2019), pp. 1510-1529.

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  • 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.

  • History

Published online: 2019-08

  • AMS Subject Headings

35K55, 65M12, 65M15, 65F30

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