Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations

In this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized steady incompressible Navier–Stokes equations with low Reynolds number. Supremizer solutions are addedto the reduced velocity space in order to obtain a stable reduced-order system, considering in particular thefulfillment of an inf-sup condition. The stability analysis is first carried out from a theoretical standpoint andthen confirmed by numerical tests performed on a parametrized two-dimensional backward-facing step flow.