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

Pressure and convection robust bounds for continuous interior penalty  divergence-free finite element methods for the incompressible Navier-Stokes  equations