An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations
文献类型：期刊论文
| 作者 | Zhang, Shuo1,2 |
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2021-08-12 |
| 页码 | 24 |
| 关键词 | biharmonic equation optimal cubic finite element scheme general triangulation discretized Stokes complex discrete strengthened Miranda-Talenti estimate |
| ISSN号 | 1674-7283 |
| DOI | 10.1007/s11425-020-1882-6 |
| 英文摘要 | This paper presents a nonconforming finite element scheme for the planar biharmonic equation, which applies piecewise cubic polynomials (P-3) and possesses O(h(2)) convergence rate for smooth solutions in the energy norm on general shape-regular triangulations. Both Dirichlet and Navier type boundary value problems are studied. The basis for the scheme is a piecewise cubic polynomial space, which can approximate the H-4 functions with O(h(2)) accuracy in the broken H-2 norm. Besides, a discrete strengthened Miranda-Talenti estimate (del(2)(h) center dot, del(2)(h) center dot) = (Delta(h) center dot, Delta h center dot), which is usually not true for nonconforming finite element spaces, is proved. The finite element space does not correspond to a finite element defined with Ciarlet's triple; however, it admits a set of locally supported basis functions and can thus be implemented by the usual routine. The notion of the finite element Stokes complex plays an important role in the analysis as well as the construction of the basis functions. |
| 资助项目 | National Natural Science Foundation of China[11871465] ; National Natural Science Foundation of China[11471026] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDB 41000000] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000684493900002 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59059]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Zhang, Shuo |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhang, Shuo. An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations[J]. SCIENCE CHINA-MATHEMATICS,2021:24. |
| APA | Zhang, Shuo.(2021).An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations.SCIENCE CHINA-MATHEMATICS,24. |
| MLA | Zhang, Shuo."An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations".SCIENCE CHINA-MATHEMATICS (2021):24. |
入库方式： OAI收割
来源：数学与系统科学研究院
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