ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION

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	ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION
	Wang, Lin 1; Yu, Haijun 2,3
	2019
发表期刊	COMMUNICATIONS IN MATHEMATICAL SCIENCES
ISSN	1539-6746
卷号	17 期号:3 页码:609-635
摘要	Phase-field model is a powerful mathematical tool to study the dynamics of interface and morphology changes in fluid mechanics and material sciences. However, numerically solving a phase field model for a real problem is a challenging task due to the non-convexity of the bulk energy and the small interface thickness parameter in the equation. In this paper, we propose two stabilized second order semi-implicit linear schemes for the Allen-Cahn phase-field equation based on backward differentiation formula and Crank-Nicolson method, respectively. In both schemes, the nonlinear bulk force is treated explicitly with two second-order stabilization terms, which make the schemes unconditionally energy stable and numerically efficient. By using a known result of the spectrum estimate of the linearized Allen-Cahn operator and some regularity estimates of the exact solution, we obtain an optimal second order convergence in time with a prefactor depending on the inverse of the characteristic interface thickness only in some lower polynomial order. Both 2-dimensional and 3-dimensional numerical results are presented to verify the accuracy and efficiency of proposed schemes.
关键词	Allen-Cahn equation energy stable stabilized semi-implicit scheme second order scheme error estimate
语种	英语
资助项目	NNSFC[11771439] ; NNSFC[U1530401] ; NNSFC[91852116] ; China National Program on Key Basic Research Project[2015CB856003]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000485624800002
出版者	INT PRESS BOSTON, INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35537
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Lin
作者单位	1.Beijing Computat Sci Res Ctr, CSRC, Beijing 100193, Peoples R China 2.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS & LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Wang, Lin,Yu, Haijun. ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION[J]. COMMUNICATIONS IN MATHEMATICAL SCIENCES,2019,17(3):609-635.
APA	Wang, Lin,&Yu, Haijun.(2019).ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION.COMMUNICATIONS IN MATHEMATICAL SCIENCES,17(3),609-635.
MLA	Wang, Lin,et al."ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION".COMMUNICATIONS IN MATHEMATICAL SCIENCES 17.3(2019):609-635.