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Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system

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Abstract

In this paper, we construct several efficient scalar auxiliary variable (SAV) schemes based on the Fourier-spectral method in space for the Cahn-Hilliard-Hele-Shaw system. The temporal discretizations are built upon the first-order Euler and second-order BDF method, respectively. We derive the unconditional energy stability for both schemes and also establish the rigorous error estimates for the first-order SAV Fourier-spectral scheme. Finally, various numerical experiments are presented to demonstrate the accuracy and performance for the constructed schemes.

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Funding

This work is supported by the National Natural Science Foundation of China under grant numbers 11901489 and 12131014.

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Authors and Affiliations

  1. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, 361005, Xiamen, Fujian, China

    Nan Zheng

  2. School of Mathematics, Shandong University, 250100, Jinan, Shandong, People’s Republic of China

    Xiaoli Li

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  1. Nan Zheng
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  2. Xiaoli Li
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Correspondence to Xiaoli Li.

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Communicated by: Silas Alben

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Zheng, N., Li, X. Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system. Adv Comput Math 47, 71 (2021). https://doi.org/10.1007/s10444-021-09897-0

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