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 SUPG-curl stabilization. A set of numerical tests, in accordance with the theoretical results, is included.