KMS Of Academy of mathematics and systems sciences, CAS
An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations | |
Zhang, Shuo1,2 | |
2021-08-12 | |
Source Publication | SCIENCE CHINA-MATHEMATICS |
ISSN | 1674-7283 |
Pages | 24 |
Abstract | 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. |
Keyword | biharmonic equation optimal cubic finite element scheme general triangulation discretized Stokes complex discrete strengthened Miranda-Talenti estimate |
DOI | 10.1007/s11425-020-1882-6 |
Indexed By | SCI |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000684493900002 |
Publisher | SCIENCE PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59060 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Zhang, Shuo |
Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
Recommended Citation 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. |
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