Mixed Virtual Elements (MVE) is an innovative class of discretization schemes allowing solution of PDEs on virtually any mesh; such schemes stem from the idea of building discrete operators mimicking certain key properties of their continuous counterparts. In our previous work [27] we implemented our own 1st-order MVE scheme for convection-diffusion. In the present work, a) we extend such scheme to formally 2nd-order accuracy, b) we deal with the subsequent stability issues, c) we derive a full formally 2nd-order MVE scheme for incompressible steady-state Navier-Stokes, d) we provide a first suggestion for a MVE N-S solution algorithm. Numerical results are reported for benchmark test cases
