KMS Of Academy of mathematics and systems sciences, CAS
| 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, Japan 2.Waseda Univ, Fac Sci & Engn, Tokyo 1698555, Japan 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China |
| Recommended Citation 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. |
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