KMS Of Academy of mathematics and systems sciences, CAS
| A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials | |
| Quan, Qimeng1; Ji, Xia2,3; Zhang, Shuo4,5 | |
| 2022-03-01 | |
| Source Publication | CALCOLO
 |
| ISSN | 0008-0624 |
| Volume | 59Issue:1Pages:32 |
| Abstract | This paper discusses finite elements defined by Ciarlet's triple on grids that consist of general quadrilaterals not limited in parallelograms. Specifically, two finite elements are established for the H-1 and H (rot) elliptic problems, respectively. An O(h) order convergence rate in energy norm for both of them and an O(h(2)) order convergence in L-2 norm for the H-1 scheme are proved under the O(h(2)) asymptotic-parallelogram assumption on the grids. Further, these two finite element spaces, together with the space of piecewise constant functions, formulate a discretized de Rham complex on general quadrilateral grids. The finite element spaces consist of piecewise polynomial functions, and, thus, are nonconforming on general quadrilateral grids. Indeed, a rigorous analysis is given in this paper that it is impossible to construct a practically useful finite element by Ciarlet's triple that can formulate a finite element space which consists of continuous piecewise polynomial functions on a grid that may include arbitrary quadrilaterals. |
| Keyword | Nonconforming finite element De Rham complex General quadrilateral grids Piecewise polynomial |
| DOI | 10.1007/s10092-021-00447-0 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11871465] ; National Natural Science Foundation of China[11471026] ; Beijing Natural Science Foundation[Z200003] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDB 41000000] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000727851500001 |
| Publisher | SPRINGER-VERLAG ITALIA SRL |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59677 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Zhang, Shuo |
| Affiliation | 1.Univ Chinese Acad Sci, Beijing 100190, Peoples R China 2.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China 3.Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Quan, Qimeng,Ji, Xia,Zhang, Shuo. A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials[J]. CALCOLO,2022,59(1):32. |
| APA | Quan, Qimeng,Ji, Xia,&Zhang, Shuo.(2022).A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials.CALCOLO,59(1),32. |
| MLA | Quan, Qimeng,et al."A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials".CALCOLO 59.1(2022):32. |
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