|Table of Contents|

Some Estimates for H1 Nonconforming Virtual Element Methods(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2021年02期
Page:
1-5
Research Field:
·数学·
Publishing date:

Info

Title:
Some Estimates for H1 Nonconforming Virtual Element Methods
Author(s):
Huang Jianguo; Yu Yue
School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China
Keywords:
nonconforming virtual element method; inverse inequality; norm equivalence; interpolation error estimate
PACS:
O24
DOI:
10.3969/j.issn.1001-4616.2021.02.001
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.

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Last Update: 2021-06-30