Convergence Analysis of Exponential Time Differencing Schemes for the Cahn-Hilliard Equation†
Convergence Analysis of Exponential Time Differencing Schemes for the Cahn-Hilliard Equation†
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DOI：
10.4208/cicp.2019.js60.12
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发表时间：
2019-06
影响因子：
3.7
通讯作者：
Xiao Li
中科院分区：
文献类型：
--
作者：
Xiao Li
本文严格证明了求解Cahn-Hilliard方程的全离散一阶和二阶指数型时间差分格式的收敛性。我们的分析主要遵循标准的程序与数值误差函数的一致性和稳定性估计，而高阶的一致性分析的技术，以获得一致的L有界性的数值解在适当的时间步长和空间网格尺寸的限制。本文为指数时间差分法的数值分析以及相场模型的其他相关数值方法提供了理论支持，这些方法通常需要一致L有界性的假设。AMS科目分类：35 K55、65 M12、65 M15、65 F30
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