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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
ISSN/eISSN0898-1221
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
DOI10.1016/j.camwa.2023.01.007
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语种英语English
Scopus入藏号2-s2.0-85146546556
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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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