KMS Of Academy of mathematics and systems sciences, CAS
| A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem | |
| Xi, Yingxia1; Ji, Xia2,3; Zhang, Shuo4 | |
| 2020-06-15 | |
| Source Publication | JOURNAL OF SCIENTIFIC COMPUTING
 |
| ISSN | 0885-7474 |
| Volume | 83Issue:3Pages:20 |
| Abstract | In this paper, we consider a cubic H-2 nonconforming finite element scheme B-h0(3) which does not correspond to a locally defined finite element with Ciarlet's triple but admit a set of local basis functions. For the first time, we deduce and write out the expression of basis functions explicitly. Distinguished from the most nonconforming finite element methods, (delta Delta(h)., Delta(h).) with non-constant coefficient delta > 0 is coercive on the nonconforming B-h0(3) space which makes it robust for numerical discretization. For fourth order eigenvalue problem, the B-h0(3) scheme can provide O(h(2)) approximation for the eigenspace in energy norm and O(h(4)) approximation for the eigenvalues. We test the B-h0(3) scheme on the vary-coefficient bi-Laplace source and eigenvalue problem, further, transmission eigenvalue problem. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed scheme. |
| Keyword | Nonconforming finite element method Transmission eigenvalues High accurary |
| DOI | 10.1007/s10915-020-01247-4 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11901295] ; National Natural Science Foundation of China[11971468] ; National Natural Science Foundation of China[91630313] ; National Natural Science Foundation of China[11471026] ; National Natural Science Foundation of China[11871465] ; Natural Science Foundation of Jiangsu Province[BK20190431] ; Start-up Fund for Scientific Research, Nanjing University of Science and Technology[AE89991/109] ; National Centre for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000544999500002 |
| Publisher | SPRINGER/PLENUM PUBLISHERS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51736 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Ji, Xia |
| Affiliation | 1.Nanjing Univ Sci & Technol, Sch Sci, Nanjing 210094, 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 |
| Recommended Citation GB/T 7714 | Xi, Yingxia,Ji, Xia,Zhang, Shuo. A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem[J]. JOURNAL OF SCIENTIFIC COMPUTING,2020,83(3):20. |
| APA | Xi, Yingxia,Ji, Xia,&Zhang, Shuo.(2020).A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem.JOURNAL OF SCIENTIFIC COMPUTING,83(3),20. |
| MLA | Xi, Yingxia,et al."A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem".JOURNAL OF SCIENTIFIC COMPUTING 83.3(2020):20. |
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