A fourth-order unfitted characteristic finite element method for free-boundary problems
文献类型：期刊论文
| 作者 | Ma, Chuwen1,2; Zheng, Weiying1,2 |
| 刊名 | JOURNAL OF COMPUTATIONAL PHYSICS
 |
| 出版日期 | 2022-11-15 |
| 卷号 | 469页码:19 |
| 关键词 | Free-boundary problems Unfitted characteristic finite element methods Convection-diffusion equation Navier-Stokes equations |
| ISSN号 | 0021-9991 |
| DOI | 10.1016/j.jcp.2022.111552 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000862984300001 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60956]  |
| 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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, LSEC,NCMIS, Beijing 100190, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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