[1]黄建国,余 跃.关于H1非协调虚拟元的若干估计[J].南京师大学报(自然科学版),2021,44(02):1-5.[doi:10.3969/j.issn.1001-4616.2021.02.001]
　Huang Jianguo,Yu Yue.Some Estimates for H1 Nonconforming Virtual Element Methods[J].Journal of Nanjing Normal University(Natural Science Edition),2021,44(02):1-5.[doi:10.3969/j.issn.1001-4616.2021.02.001]
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关于H1非协调虚拟元的若干估计()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第44卷
期数:
2021年02期
页码:
1-5
栏目:
·数学·
出版日期:
2021-06-30

文章信息/Info

Title:
Some Estimates for H1 Nonconforming Virtual Element Methods
文章编号:
1001-4616(2021)02-0001-05
作者:
黄建国; 余 跃
上海交通大学数学科学学院,上海 200240
Author(s):
Huang Jianguo; Yu Yue
School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China
关键词:
非协调虚拟元方法; 逆不等式; 范数等价性; 插值误差估计
Keywords:
nonconforming virtual element method; inverse inequality; norm equivalence; interpolation error estimate
分类号:
O24
DOI:
10.3969/j.issn.1001-4616.2021.02.001
文献标志码:
A
摘要:
本文在多角形网格具拟一致、正则虚拟三角剖分的假设下建立了H1非协调虚拟元的若干估计,包括逆不等式、范数等价性和插值误差估计. 首先用证明协调虚拟元逆不等式的方法在虚拟三角形上使用泡函数技巧获得逆不等式. 然后证明自由度型的逆不等式和Poincare-Friedrichs不等式,据此获得L2型范数等价性中关键的上界估计. 最后利用范数等价性,给出插值算子误差分析的统一方法,即先建立插值算子的稳定性,再使用Bramble-Hilbert论证获得最优误差估计.
Abstract:
This paper develops some estimates for the H1 nonconforming virtual element methods(VEMs)including inverse inequality,norm equivalence,and interpolation error estimate related to polygonal meshes,each of which admits a virtual quasi-uniform and regular triangulation. We first derive the inverse inequality by using the arguments for proving the inverse inequality of conforming VEMs and the bubble function technique. Next,we obtain the inverse inequality and the Poincare-Friedrichs inequality involving the degrees of freedom of a VEM function,which lead to the critical estimate of the upper bound of the L2 case in the norm equivalence. In view of the stability result of the interpolation operator established in advance,we finally obtain a unified error analysis of interpolation operators using the Bramble-Hilbert argument.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2020-11-15.
基金项目:国家自然科学基金面上项目(12071289).
通讯作者:余跃,博士研究生,研究方向:科学计算. E-mail:terenceyuyue@sjtu.edu.cn
更新日期/Last Update: 2021-06-30