A fourth-order unfitted characteristic finite element method for free-boundary problems

doi:10.1016/j.jcp.2022.111552

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	A fourth-order unfitted characteristic finite element method for free-boundary problems
	Ma, Chuwen 1,2; Zheng, Weiying 1,2
	2022-11-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	469 页码:19
摘要	A fourth-order unfitted characteristic finite element method (UCFEM) is proposed to solve free-boundary problems of time-dependent partial differential equations (PDEs). The boundary of the domain is implicitly driven by the solution of the PDE, while the PDE is proposed on the time-varying unknown domain. In this way, they form a coupled nonlinear system. The key ingredient of the UCFEM is to trace the domain explicitly with a fourth -order forward flow map and discretize the PDE in time with a fourth-order backward flow map. The PDE is solved with a fourth-order unfitted finite element method on a fixed mesh. Since the boundary of the domain is expressed explicitly with cubic spline functions, quadrature on cut elements can be done accurately and efficiently even the domain undergoes severe deformations. The UCFEM provides a framework of designing high-order numerical methods for free-boundary problems. We apply the UCFEM to a two-dimensional convection-diffusion equation and Navier-Stokes equations, and obtain the overall fourth order of accuracy. With extensive numerical experiments, we show that the proposed method can achieve the fourth-order convergence even on severely deformed domains. (C) 2022 Elsevier Inc. All rights reserved.
关键词	Free-boundary problems Unfitted characteristic finite element methods Convection-diffusion equation Navier-Stokes equations
DOI	10.1016/j.jcp.2022.111552
收录类别	SCI
语种	英语
资助项目	National Science Fund for Distinguished Young Scholars[11725106] ; China NSF[12126372] ; China NSF[11831016]
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000862984300001
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60957
专题	中国科学院数学与系统科学研究院
通讯作者	Zheng, Weiying
作者单位	1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, LSEC,NCMIS, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Ma, Chuwen,Zheng, Weiying. A fourth-order unfitted characteristic finite element method for free-boundary problems[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2022,469:19.
APA	Ma, Chuwen,&Zheng, Weiying.(2022).A fourth-order unfitted characteristic finite element method for free-boundary problems.JOURNAL OF COMPUTATIONAL PHYSICS,469,19.
MLA	Ma, Chuwen,et al."A fourth-order unfitted characteristic finite element method for free-boundary problems".JOURNAL OF COMPUTATIONAL PHYSICS 469(2022):19.