KMS Of Academy of mathematics and systems sciences, CAS
| Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems | |
Chen, Huangxin1; Xu, Xuejun1 ; Hoppe, Ronald H. W.2,3
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| 2010-09-01 | |
| Source Publication | NUMERISCHE MATHEMATIK
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| ISSN | 0029-599X |
| Volume | 116Issue:3Pages:383-419 |
| Abstract | Recently an adaptive nonconforming finite element method (ANFEM) has been developed by Carstensen and Hoppe (in Numer Math 103:251-266, 2006). In this paper, we extend the result to some nonsymmetric and indefinite problems. The main tools in our analysis are a posteriori error estimators and a quasi-orthogonality property. In this case, we need to overcome two main difficulties: one stems from the nonconformity of the finite element space, the other is how to handle the effect of a nonsymmetric and indefinite bilinear form. An appropriate adaptive nonconforming finite element method featuring a marking strategy based on the comparison of the a posteriori error estimator and a volume term is proposed for the lowest order Crouzeix-Raviart element. It is shown that the ANFEM is a contraction for the sum of the energy error and a scaled volume term between two consecutive adaptive loops. Moreover, quasi-optimality in the sense of quasi-optimal algorithmic complexity can be shown for the ANFEM. The results of numerical experiments confirm the theoretical findings. |
| DOI | 10.1007/s00211-010-0307-6 |
| Language | 英语 |
| Funding Project | NSF[DMS-0511624] ; NSF[DMS-0707602] ; NSF[DMS-0810176] ; NSF[DMS-0811153] ; NSF[DMS-0914788] ; National Science Foundation (NSF) of China[10731060] ; Special funds for major state basic research projects (973)[2005CB321701] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000281397600002 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/10716 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Chen, Huangxin |
| Affiliation | 1.Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Augsburg, Inst Math, D-86159 Augsburg, Germany 3.Univ Houston, Dept Math, Houston, TX 77204 USA |
| Recommended Citation GB/T 7714 | Chen, Huangxin,Xu, Xuejun,Hoppe, Ronald H. W.. Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems[J]. NUMERISCHE MATHEMATIK,2010,116(3):383-419. |
| APA | Chen, Huangxin,Xu, Xuejun,&Hoppe, Ronald H. W..(2010).Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems.NUMERISCHE MATHEMATIK,116(3),383-419. |
| MLA | Chen, Huangxin,et al."Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems".NUMERISCHE MATHEMATIK 116.3(2010):383-419. |
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