  In this paper we analyze a pressure-robust method based on divergence-free
mixed finite element methods with continuous interior penalty stabilization.
The main goal is to prove an $O(h^{k+1/2})$ error estimate for the $L^2$ norm
of the velocity in the convection dominated regime. This bound is pressure
robust (the error bound of the velocity does not depend on the pressure) and
also convection robust (the constants in the error bounds are independent of
the Reynolds number).
