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A Large Time-Stepping Mixed Finite Method of the Modified Cahn–Hilliard Equation

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Abstract

The main purpose of this paper is to solve the modified Cahn–Hilliard equation via a large time-stepping mixed finite-element method to ease the time-stepping limit caused by small parameters and nonlinear terms. The modified Cahn–Hilliard equation is discretized by mixed finite-element method in space and first-order semi-implicit scheme in time. The energy stability and error analysis of the fully discrete semi-implicit scheme are proved. Finally, a series of numerical experiments are presented to verify the conclusion of theoretical part.

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Authors and Affiliations

  1. College of Mathematics, Taiyuan University of Technology, Tai’yuan, 030024, China

    Hongen Jia, Huanhuan Hu & Lingxiong Meng

  2. School of Mathematics and Computational Science, Xiangtan University, Xiang’tan, 411105, China

    Hongen Jia

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  1. Hongen Jia
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  2. Huanhuan Hu
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  3. Lingxiong Meng
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Correspondence to Hongen Jia.

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Communicated by Davod Khojasteh Salkuyeh.

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Supported by the National Nature Foundation of China (No. 11872264), the Provincial Natural Science Foundation of Shanxi (No. 201901D111123), Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (No. 2017119), Key Research and Development (R&D) Projects of Shanxi Province (No. 201903D121038).

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Jia, H., Hu, H. & Meng, L. A Large Time-Stepping Mixed Finite Method of the Modified Cahn–Hilliard Equation. Bull. Iran. Math. Soc. 46, 1551–1569 (2020). https://doi.org/10.1007/s41980-019-00342-z

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  • DOI: https://doi.org/10.1007/s41980-019-00342-z

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