Anisotropic Error Estimates of The Linear Nonconforming Virtual Element Methods
This work provides theoretical error bounds for nonconforming VEM on anisotropic meshes, which is important for numerical analysts working on polytopal mesh methods.
The paper develops refined a priori error estimates for the lowest order nonconforming Virtual Element Method for Poisson problems in 2D and 3D, introducing new geometric assumptions and a stabilization technique for anisotropic elements.
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.