  We construct new first- and second-order pressure correction schemes using
the scalar auxiliary variable (SAV) approach for the Navier-Stokes equations.
These schemes are linear, decoupled and only require a sequence of solving
Poisson type equations at each time step. Furthermore, they are unconditionally
energy stable. We also establish rigorous error estimates for the velocity and
pressure approximation of the first-order scheme without any condition on the
time step.

Numerical Analysis;Numerical Analysis;Analysis of PDEs