The 3D Nonconforming Virtual Element Method with enhanced spaces: numerical investigation and implementation guide

Abstract

In this paper, we describe the 3D Nonconforming Virtual Element Method, where the local spaces are enhanced in order to build an $L^2$ projection of virtual functions onto polynomials of degree $k$. This higher order projection provides a more accurate representation of the load term and, more importantly, it enables the construction of the reaction term. We conduct a convergence analysis of the $L^2$ norm and $H^1$ seminorm errors with respect to mesh size and approximation degree. We also compare our results with those obtained using the conforming Virtual Element Method.