Towards pressure-robust mixed methods for the incompressible navier–stokes equations

Abstract

When mixed methods for the incompressible Navier–Stokes were introduced in the early 70ies, it was claimed that the divergence-constraint could be relaxed without danger. Recently, this claim has been challenged. Therefore, we review the numerical error analysis of mixed methods and show that divergence-free/pressure-robust mixed methods behave in a provably much more robust way.