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Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation

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Abstract

In this paper, we construct efficient schemes based on the scalar auxiliary variable block-centered finite difference method for the modified phase field crystal equation, which is a sixth-order nonlinear damped wave equation. The schemes are linear, conserve mass and unconditionally dissipate a pseudo energy. We prove rigorously second-order error estimates in both time and space for the phase field variable in discrete norms. We also present some numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy.

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Acknowledgements

The first author was supported by National Natural Science Foundation of China (Grant Nos. 11901489 and 11971407). The second author was supported by National Science Foundation of USA (Grant No. DMS-1720442).

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Xiaoli Li

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Jie Shen

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  1. Xiaoli Li
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  2. Jie Shen
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Correspondence to Jie Shen.

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Li, X., Shen, J. Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation. Sci. China Math. 65, 2201–2218 (2022). https://doi.org/10.1007/s11425-020-1867-8

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  • DOI: https://doi.org/10.1007/s11425-020-1867-8

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