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On the energy stability of Strang-splitting for Cahn-Hilliard

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arxiv 2107.05349 v1 pith:SRWRZ5LH submitted 2021-07-12 math.NA cs.NAmath.AP

Dong Li , Chaoyu Quan This is my paper · ORCID
classification math.NAcs.NAmath.AP
keywords cahn-hilliardstabilityenergyequationoperator-splittingordersecondcheng
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We consider a Strang-type second order operator-splitting discretization for the Cahn-Hilliard equation. We introduce a new theoretical framework and prove uniform energy stability of the numerical solution and persistence of all higher Sobolev norms. This is the first strong stability result for second order operator-splitting methods for the Cahn-Hilliard equation. In particular we settle several long-standing open issues in the work of Cheng, Kurganov, Qu and Tang \cite{Tang15}.

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  1. An exponential-free Runge--Kutta framework for developing third-order unconditionally energy stable schemes for the Cahn--Hilliard equation

    math.NA 2024-11 conditional novelty 6.0 of 10

    Taylor-polynomial based exponential-free Runge-Kutta schemes for the Cahn-Hilliard equation give up to third-order, equilibrium-preserving, unconditionally energy stable time integration.

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