, 55:5 | Cite as

Some error analysis on virtual element methods



Some error analyses on virtual element methods (VEMs) including inverse inequalities, norm equivalence, and interpolation error estimates are developed for polygonal meshes, each element of which admits a virtual quasi-uniform triangulation. This sub-mesh regularity covers the usual ones used for theoretical analysis of VEMs, and the proofs are presented by means of standard technical tools in finite element methods.


Virtual elements Inverse inequality Norm equivalence Interpolation error estimate 

Mathematics Subject Classification

65N30 65N12 



We thank the referees for valuable suggestions and comments which improved an early version of the paper. The first author was supported by the National Science Foundation (NSF) DMS-1418934 and in part by the Sea Poly Project of Beijing Overseas Talents. The second author was partially supported by NSFC (Grant No. 11571237).


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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at IrvineIrvineUSA
  2. 2.Beijing Institute for Scientific and Engineering ComputingBeijing University of TechnologyBeijingChina
  3. 3.School of Mathematical Sciences, MOE-LSCShanghai Jiao Tong UniversityShanghaiChina

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