This paper studies non inf-sup stable nite element approximations to the evolutionary
Navier{Stokes equations. Several local projection stabilization (LPS) methods corresponding
to di erent stabilization terms are analyzed, thereby separately studying the e ects of
the di erent stabilization terms. Error estimates are derived in which the constants in the
error bounds are independent of inverse powers of the viscosity. For one of the methods,
using velocity and pressure nite elements of degree l, it will be proved that the velocity
error in L1(0; T;L2(
)) decays with rate l + 1=2 in the case that h, with being
the dimensionless viscosity and h the mesh width. In the analysis of another method, it
was observed that the convective term can be bounded in an optimal way with the LPS
stabilization of the pressure gradient. Numerical studies con rm the analytical results.
