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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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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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  • DOI: https://doi.org/10.1007/s10444-021-09897-0

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