Anisotropic Error Estimates of The Linear Nonconforming Virtual Element Methods
Numerical Analysis
2019-05-17 v2
Abstract
A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape regularity of polytopal meshes. A new error equation for the lowest order (linear) nonconforming VEM is derived for any choice of stabilization, and a new stabilization using a projection on an extended element patch is introduced for the error analysis on anisotropic elements.
Cite
@article{arxiv.1806.09054,
title = {Anisotropic Error Estimates of The Linear Nonconforming Virtual Element Methods},
author = {Shuhao Cao and Long Chen},
journal= {arXiv preprint arXiv:1806.09054},
year = {2019}
}