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An efficient data assimilation based unconditionally stable scheme for Cahn–Hilliard equation

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Abstract

This paper aims to present an efficient numerical method for solving the Cahn–Hilliard equation incorporating a data assimilation term. The data assimilation term employs a feedback control strategy to guide the computational solution towards the observed data. The Crank–Nicolson formula is employed for discretizing the equation system, while a scalar auxiliary variable approach is adopted to ensure energy dissipation preservation. The proposed scheme attains second-order accuracy in both temporal and spatial dimensions. The unconditional energy stability of the scheme is proven theoretically. Numerous numerical experiments are conducted to illustrate the efficacy of the proposed scheme.

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Availability of data and materials

The data used in this paper are available at https://github.com/xjtu-songxin/dataset-for-CH-equation-with-data-assimilation-method.git.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (No. 12271430) and Scientific Research Fund for High-level Talents of Xijing University (No. XJ23B08). The authors would like to thank the reviewers for their constructive and helpful comments regarding the revision of this article.

Funding

This work is supported by Natural Science Basic Research Program of Shaanxi (No. 2024JC-YBMS-016) and by Scientific Research Fund for High-level Talents of Xijing University (No. XJ23B08).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an, 710049, Shannxi, China

    Xin Song & Yibao Li

  2. School of Computer Science, Xijing University, Xi’an, 710049, Shannxi, China

    Binhu Xia

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  1. Xin Song
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  2. Binhu Xia
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Song, X., Xia, B. & Li, Y. An efficient data assimilation based unconditionally stable scheme for Cahn–Hilliard equation. Comp. Appl. Math. 43, 121 (2024). https://doi.org/10.1007/s40314-024-02632-7

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