{"title":"A Scalar Auxiliary Variable (SAV) Finite Element Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Dynamic Boundary Conditions","authors":"C. Yao, Feng Wang","doi":"10.4208/jcm.2205-m2021-0234","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the Cahn-Hilliard-Hele-Shaw (CHHS) system with the dynamic boundary conditions, in which both the bulk and surface energy parts play important roles. The scalar auxiliary variable (SAV) approach is introduced for the physical system; the mass conservation and energy dissipation is proved for the CHHS system. Subsequently, a fully discrete SAV finite element scheme is proposed, with the mass conservation and energy dissipation laws established at a theoretical level. In addition, the convergence analysis and error estimate is provided for the proposed SAV numerical scheme.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jcm.2205-m2021-0234","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we consider the Cahn-Hilliard-Hele-Shaw (CHHS) system with the dynamic boundary conditions, in which both the bulk and surface energy parts play important roles. The scalar auxiliary variable (SAV) approach is introduced for the physical system; the mass conservation and energy dissipation is proved for the CHHS system. Subsequently, a fully discrete SAV finite element scheme is proposed, with the mass conservation and energy dissipation laws established at a theoretical level. In addition, the convergence analysis and error estimate is provided for the proposed SAV numerical scheme.
期刊介绍：
Journal of Computational Mathematics (JCM) is an international scientific computing journal founded by Professor Feng Kang in 1983, which is the first Chinese computational mathematics journal published in English. JCM covers all branches of modern computational mathematics such as numerical linear algebra, numerical optimization, computational geometry, numerical PDEs, and inverse problems. JCM has been sponsored by the Institute of Computational Mathematics of the Chinese Academy of Sciences.
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