Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations

doi:10.1007/s13160-020-00449-5

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	Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations
	Liu, Xuefeng 1; Nakao, Mitsuhiro T.2; You, Chun'guang 3; Oishi, Shin'ichi 2
	2021-01-02
发表期刊	JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
ISSN	0916-7005
页码	15
摘要	For the Stokes equation over 2D and 3D domains, explicit a posteriori and a priori error estimation are novelly developed for the finite element solution. The difficulty in handling the divergence-free condition of the Stokes equation is solved by utilizing the extended hypercircle method along with the Scott-Vogelius finite element scheme. Since all terms in the error estimation have explicit values, by further applying the interval arithmetic and verified computing algorithms, the computed results provide rigorous estimation for the approximation error. As an application of the proposed error estimation, the eigenvalue problem of the Stokes operator is considered and rigorous bounds for the eigenvalues are obtained. The efficiency of proposed error estimation is demonstrated by solving the Stokes equation on both convex and non-convex 3D domains.
关键词	Stokes equation A posteriori error estimation A priori error estimation Finite element method Hypercircle method Eigenvalue problem
DOI	10.1007/s13160-020-00449-5
收录类别	SCI
语种	英语
资助项目	Japan Society for the Promotion of Science[16H03950] ; Japan Society for the Promotion of Science[20H01820] ; Japan Society for the Promotion of Science[18K03411] ; JST CREST, Japan[JPMJCR14D4] ; [18K03434]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000604171900001
出版者	SPRINGER JAPAN KK
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57944
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Xuefeng
作者单位	1.Niigata Univ, Grad Sch Sci & Technol, Niigata 9502181, Japan 2.Waseda Univ, Fac Sci & Engn, Tokyo 1698555, Japan 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Liu, Xuefeng,Nakao, Mitsuhiro T.,You, Chun'guang,et al. Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations[J]. JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS,2021:15.
APA	Liu, Xuefeng,Nakao, Mitsuhiro T.,You, Chun'guang,&Oishi, Shin'ichi.(2021).Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations.JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS,15.
MLA	Liu, Xuefeng,et al."Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations".JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS (2021):15.