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

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 se...

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Bibliographic Details
Published inarXiv.org
Main Authors Li, Dong, Quan, Chaoyu
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.07.2021
Subjects
Norms
Splitting
Stability
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Summary: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}.
ISSN:2331-8422