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

In this paper, we present the implementation details of the three-dimensional Nonconforming Virtual Element Method, building upon the theoretical framework introduced in (ESAIM: Math. Model. Numer. Anal., 50(3), 879–904, (2016), (IMA J. Numer. Anal., 37, (2015). In this formulation, the local spaces are suitably enhanced to allow the construction of the projection of virtual functions onto polynomials of degree. This higher-order projection provides a more accurate representation of the load term and, more importantly, enables the definition of the reaction term. We perform a numerical convergence study of the -norm and -seminorm errors with respect to both mesh size and polynomial degree in the three-dimensional setting. Numerical results are then compared with those obtained using the conforming VEM, showing the consistency and computational performance of the proposed 3D implementation.