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Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal Equation

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Abstract

In this paper, we propose a second-order fast explicit operator splitting method for the phase field crystal equation. The basic idea lied in our method is to split the original problem into linear and nonlinear parts. The linear subproblem is numerically solved using the Fourier spectral method, which is based on the exact solution and thus has no stability restriction on the time-step size. The nonlinear one is solved via second-order strong stability preserving Runge–Kutta method. The stability and convergence are discussed in \(L^2\)-norm. Numerical experiments are performed to validate the accuracy and efficiency of the proposed method. Moreover, energy degradation and mass conservation are also verified.

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Acknowledgements

The authors would like to thank the editor and referees for their valuable comments and suggestions which helped us to improve the results of this paper. This work is in part supported by the National Natural Science Foundation of China (Nos. 11701196 and 11701197), the Natural Science Foundation of Fujian Province(No. 2020J01074), and the Fundamental Research Funds for the Central Universities (No. ZQN-702).

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Authors and Affiliations

  1. Fujian Province University Key Laboratory of Computation Science, School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, People’s Republic of China

    Shuying Zhai & Zhifeng Weng

  2. College of Mathematics and Systems Science, Xinjiang University, Ürümqi, 830046, People’s Republic of China

    Xinlong Feng

  3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Yinnian He

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  1. Shuying Zhai
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Correspondence to Yinnian He.

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Zhai, S., Weng, Z., Feng, X. et al. Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal Equation. J Sci Comput 86, 8 (2021). https://doi.org/10.1007/s10915-020-01386-8

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