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A three level linearized compact difference scheme for the Cahn-Hilliard equation

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Abstract

This article is devoted to the study of high order accuracy difference methods for the Cahn-Hilliard equation. A three level linearized compact difference scheme is derived. The unique solvability and unconditional convergence of the difference solution are proved. The convergence order is O(τ 2 + h 4) in the maximum norm. The mass conservation and the non-increase of the total energy are also verified. Some numerical examples are given to demonstrate the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Juan Li, ZhiZhong Sun & Xuan Zhao

  2. Yingtian College, Nanjing, 210046, China

    Juan Li

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  1. Juan Li
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  2. ZhiZhong Sun
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  3. Xuan Zhao
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Correspondence to ZhiZhong Sun.

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Li, J., Sun, Z. & Zhao, X. A three level linearized compact difference scheme for the Cahn-Hilliard equation. Sci. China Math. 55, 805–826 (2012). https://doi.org/10.1007/s11425-011-4290-x

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  • DOI: https://doi.org/10.1007/s11425-011-4290-x

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