High-order Virtual Element Method on polyhedral meshes

We develop a numerical assessment of the Virtual Element Method for the discretization of a diffusion–reaction model problem, for higher “polynomial” order k and three space dimensions. Although the main focus of the present study is to illustrate some h-convergence tests for different orders k, we also hint on other interesting aspects such as structured polyhedral Voronoi meshing, robustness in the presence of irregular grids, sensibility to the stabilization parameter and convergence with respect to the order k.