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

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

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