  We analyse the p- and hp-versions of the virtual element method (VEM) for the
the Stokes problem on a polygonal domain. The key tool in the analysis is the
existence of a bijection between Poisson-like and Stokes-like VE spaces for the
velocities. This allows us to re-interpret the standard VEM for Stokes as a
VEM, where the test and trial discrete velocities are sought in Poisson-like VE
spaces. The upside of this fact is that we inherit from [7] an explicit
analysis of best interpolation results in VE spaces, as well as stabilization
estimates that are explicit in terms of the degree of accuracy of the method.
We prove exponential convergence of the hp-VEM for Stokes problems with regular
right-hand sides. We corroborate the theoretical estimates with numerical tests
for both the p- and hp-versions of the method.
