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 Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations Liu, Xuefeng1; Nakao, Mitsuhiro T.2; You, Chun'guang3; Oishi, Shin'ichi2 2021-01-02 Source Publication JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS ISSN 0916-7005 Pages 15 Abstract 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. Keyword Stokes equation A posteriori error estimation A priori error estimation Finite element method Hypercircle method Eigenvalue problem DOI 10.1007/s13160-020-00449-5 Indexed By SCI Language 英语 Funding Project 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 Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000604171900001 Publisher SPRINGER JAPAN KK Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/57944 Collection 中国科学院数学与系统科学研究院 Corresponding Author Liu, Xuefeng Affiliation 1.Niigata Univ, Grad Sch Sci & Technol, Niigata 9502181, Japan2.Waseda Univ, Fac Sci & Engn, Tokyo 1698555, Japan3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China Recommended CitationGB/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.
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