题名 | Global L2 superconvergence of the tetrahedral quadratic finite element |
作者 | |
发表日期 | 2023-03-01 |
发表期刊 | Computers and Mathematics with Applications
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ISSN/eISSN | 0898-1221 |
卷号 | 133页码:104-123 |
摘要 | This paper provides the global L superconvergence of the tetrahedral quadratic finite element ‖u−u‖≤Ch‖u‖, where u and u are the finite element approximation and the quadratic Lagrange interpolation of the exact solution u respectively. The standard analysis of the global L superconvergence is combined with the weak estimate of the second type (WE2). However, the WE2 of the tetrahedral quadratic finite element has kept absent for a rather long time. To this end, we define the four-element-based uniform tetrahedral mesh, and then present the simplified weak estimate of the second type (SWE2), which simplifies the result of the WE2 and can also derive the global L superconvergence. For the completeness, the proof of the WE2 can be found in the appendix. Finally, this supercloseness will be used to construct a post-processing that increases the order of approximation to the exact solution in L norm. Numerical experiments are provided to illustrate our theoretical results. |
关键词 | Finite element Four-element-based uniform L2 superconvergence Simplified weak estimate of the second type Tetrahedral mesh |
DOI | 10.1016/j.camwa.2023.01.007 |
URL | 查看来源 |
语种 | 英语English |
Scopus入藏号 | 2-s2.0-85146546556 |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | https://repository.uic.edu.cn/handle/39GCC9TT/11594 |
专题 | 个人在本单位外知识产出 |
通讯作者 | Li,Yonghai |
作者单位 | 1.School of Mathematics,Jilin University,Changchun,130012,China 2.BNU-UIC Research Center for Mathematics,Beijing Normal University,Zhuhai,519087,China |
推荐引用方式 GB/T 7714 | Yang,Peng,Li,Yonghai,Wang,Xiang. Global L2 superconvergence of the tetrahedral quadratic finite element[J]. Computers and Mathematics with Applications, 2023, 133: 104-123. |
APA | Yang,Peng, Li,Yonghai, & Wang,Xiang. (2023). Global L2 superconvergence of the tetrahedral quadratic finite element. Computers and Mathematics with Applications, 133, 104-123. |
MLA | Yang,Peng,et al."Global L2 superconvergence of the tetrahedral quadratic finite element". Computers and Mathematics with Applications 133(2023): 104-123. |
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