  The Virtual Element Method (VEM) is a Galerkin approximation method that
extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we
present a conforming formulation that generalizes the Scott-Vogelius finite
element method for the numerical approximation of the Stokes problem to
polygonal meshes in the framework of the virtual element method. In particular,
we consider a straightforward application of the virtual element approximation
space for scalar elliptic problems to the vector case and approximate the
pressure variable through discontinuous polynomials. We assess the
effectiveness of the numerical approximation by investigating the convergence
on a manufactured solution problem and a set of representative polygonal
meshes. We numerically show that this formulation is convergent with optimal
convergence rates except for the lowest-order case on triangular meshes, where
the method coincides with the $P_1-P_0$ Scott-Vogelius scheme, and on square
meshes, which are situations that are well-known to be unstable.

Numerical Analysis;Numerical Analysis