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On Second Order Semi-implicit Fourier Spectral Methods for 2D Cahn–Hilliard Equations

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Abstract

We consider several seconder order in time stabilized semi-implicit Fourier spectral schemes for 2D Cahn–Hilliard equations. We introduce new stabilization techniques and prove unconditional energy stability for modified energy functionals. We also carry out a comparative study of several classical stabilization schemes and identify the corresponding stability regions. In several cases the energy stability is proved under relaxed constraints on the size of the time steps. We do not impose any Lipschitz assumption on the nonlinearity. The error analysis is obtained under almost optimal regularity assumptions.

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Acknowledgments

D. Li was supported by an Nserc discovery grant. The research of Z. Qiao is partially supported by the Hong Kong Research Council GRF Grant 15302214, NSFC/RGC Joint Research Scheme N_HKBU204/12 and the Hong Kong Polytechnic University internal Grant 1-ZE33.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T1Z2, Canada

    Dong Li

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong

    Zhonghua Qiao

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  1. Dong Li
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  2. Zhonghua Qiao
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Correspondence to Zhonghua Qiao.

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Li, D., Qiao, Z. On Second Order Semi-implicit Fourier Spectral Methods for 2D Cahn–Hilliard Equations. J Sci Comput 70, 301–341 (2017). https://doi.org/10.1007/s10915-016-0251-4

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  • DOI: https://doi.org/10.1007/s10915-016-0251-4

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