We consider a model Poisson problem in Rd (d=2,3) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges (d=2) or small faces (d=3).
@article{arxiv.1710.00442,
title = {Virtual Element Methods on Meshes with Small Edges or Faces},
author = {Susanne C. Brenner and Li-yeng Sung},
journal= {arXiv preprint arXiv:1710.00442},
year = {2017}
}