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The Operator-Splitting Method for Cahn-Hilliard is Stable

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Abstract

We prove energy stability of a standard operator-splitting method for the Cahn-Hilliard equation. We establish uniform bound of Sobolev norms of the numerical solution and convergence of the splitting approximation. This is the first energy stability result for the operator-splitting method for the Cahn-Hilliard equation. Our analysis can be extended to many other models.

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Notes

  1. We thank the anonymous referee for pointing this out.

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Authors and Affiliations

  1. Department of Mathematics, SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China

    Dong Li

  2. SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, China

    Chaoyu Quan

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  1. Dong Li
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  2. Chaoyu Quan
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Correspondence to Dong Li.

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Li, D., Quan, C. The Operator-Splitting Method for Cahn-Hilliard is Stable. J Sci Comput 90, 62 (2022). https://doi.org/10.1007/s10915-021-01740-4

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  • DOI: https://doi.org/10.1007/s10915-021-01740-4

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