关于H^(1)非协调虚拟元的若干估计  

Some Estimates for H^(1) Nonconforming Virtual Element Methods

作　　者：黄建国 余跃 Huang Jianguo;Yu Yue(School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学数学科学学院,上海200240

出　　处：《南京师大学报（自然科学版）》2021年第2期1-5,共5页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金面上项目(12071289).

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H^(1)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L^(2)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.This paper develops some estimates for the H^(1) 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 L^(2) 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.

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 

分 类 号：O24[理学—计算数学]