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On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation
Wang, Lin1,2; Yu, Haijun1,2
2018-11-01
Source PublicationJOURNAL OF SCIENTIFIC COMPUTING
ISSN0885-7474
Volume77Issue:2Pages:1185-1209
AbstractEfficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit schemes for the Cahn-Hilliard phase-field equation. One uses backward differentiation formula and the other uses Crank-Nicolson method to discretize linear terms. In both schemes, the nonlinear bulk forces are treated explicitly with two second-order stabilization terms. This treatment leads to linear elliptic systems with constant coefficients, for which lots of robust and efficient solvers are available. The discrete energy dissipation properties are proved for both schemes. Rigorous error analysis is carried out to show that, when the time step-size is small enough, second order accuracy in time is obtained with a prefactor controlled by a fixed power of , where is the characteristic interface thickness. Numerical results are presented to verify the accuracy and efficiency of proposed schemes.
KeywordPhase field model Cahn-Hilliard equation Energy stable Stabilized semi-implicit scheme Second order time marching
DOI10.1007/s10915-018-0746-2
Language英语
Funding ProjectNNSFC[11771439] ; NNSFC[11371358] ; NNSFC[91530322]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000446594600022
PublisherSPRINGER/PLENUM PUBLISHERS
Citation statistics
Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31454
Collection计算数学与科学工程计算研究所
Affiliation1.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS & LSEC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Wang, Lin,Yu, Haijun. On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation[J]. JOURNAL OF SCIENTIFIC COMPUTING,2018,77(2):1185-1209.
APA Wang, Lin,&Yu, Haijun.(2018).On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation.JOURNAL OF SCIENTIFIC COMPUTING,77(2),1185-1209.
MLA Wang, Lin,et al."On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation".JOURNAL OF SCIENTIFIC COMPUTING 77.2(2018):1185-1209.
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