Pressure robust SUPG-stabilized finite elements for the unsteady Navier-Stokes equation

In the present contribution, we propose a novel conforming finite element scheme for the time-dependent Navier–Stokes equation, which is proven to be both convection quasi-robust and pressure robust. The method is built combining a ‘divergence-free’ velocity/pressure couple (such as the Scott–Vogelius element), a discontinuous Galerkin in time approximation and a suitable streamline upwind Petrov–Galerkin-curl stabilization. A set of numerical tests, in accordance with the theoretical results, is included.