南方科技大学知识苑(SUSTech KC): UNIFORM L-p-BOUND OF THE ALLEN-CAHN EQUATION AND ITS NUMERICAL DISCRETIZATION

题名	UNIFORM L-p-BOUND OF THE ALLEN-CAHN EQUATION AND ITS NUMERICAL DISCRETIZATION
作者	Yang, Jiang1 ; Du, Qiang 2; Zhang, Wei 3,4
通讯作者	Zhang, Wei
发表日期	2018
发表期刊	International Journal of Numerical Analysis and Modeling 影响因子和分区
ISSN	1705-5105
卷号	15 期号:1-2页码:213-227
摘要	We study uniform bounds associated with the Allen-Cahn equation and its numerical discretization schemes. These uniform bounds are different from, and weaker than, the conventional energy dissipation and the maximum principle, but they can be helpful in the analysis of numerical methods. In particular, we show that finite difference spatial discretization, like the original continuum model, shares the uniform L-p-bound for all even p, which also leads to the maximum principle. In comparison, a couple of other spatial discretization schemes, namely the Fourier spectral Galerkin method and spectral collocation method preserve the L-p-bound only for p = 2. Moreover, fully discretized schemes based on the Fourier collocation method for spatial discretization and Strang splitting method for time discretization also preserve the uniform L-2-bound unconditionally.
关键词	Allen-Cahn Equations maximum principle operator splitting uniform L-p-bound Fourier spectral methods
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	第一
资助项目	[NSFC-91630207]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000428719500012
出版者	ISCI-INST SCIENTIFIC COMPUTING & INFORMATION
来源库	Web of Science
引用统计	被引频次[WOS]：25
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/28280
专题	理学院_数学系工学院_材料科学与工程系
作者单位	1.Southern Univ Sci & Technol, Dept Math, Shenzhen, Guangdong, Peoples R China 2.Columbia Univ, Dept Appl Phys & Appl Math, New York, NY USA 3.Beijing Computat Sci Res Ctr, Beijing, Peoples R China 4.Hong Kong Baptist Univ, Beijing Normal Univ, United Int Coll, Div Sci & Technol, Zhultai, Guangdong, Peoples R China
第一作者单位	数学系
第一作者的第一单位	数学系
推荐引用方式 GB/T 7714	Yang, Jiang,Du, Qiang,Zhang, Wei. UNIFORM L-p-BOUND OF THE ALLEN-CAHN EQUATION AND ITS NUMERICAL DISCRETIZATION[J]. International Journal of Numerical Analysis and Modeling,2018,15(1-2):213-227.
APA	Yang, Jiang,Du, Qiang,&Zhang, Wei.(2018).UNIFORM L-p-BOUND OF THE ALLEN-CAHN EQUATION AND ITS NUMERICAL DISCRETIZATION.International Journal of Numerical Analysis and Modeling,15(1-2),213-227.
MLA	Yang, Jiang,et al."UNIFORM L-p-BOUND OF THE ALLEN-CAHN EQUATION AND ITS NUMERICAL DISCRETIZATION".International Journal of Numerical Analysis and Modeling 15.1-2(2018):213-227.