Published

Anisotropic Error Estimates of The Linear Nonconforming Virtual Element Methods

Shuhao Cao and Long Chen

SIAM Journal on Numerical Analysis. 57(3): 1058-1081, 2019.

pdf   Bibtex

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.