  We introduce improved Reduced Order Models (ROM) for convection-dominated
flows. These non-linear closure models are inspired from successful numerical
stabilization techniques used in Large Eddy Simulations (LES), such as Local
Projection Stabilization (LPS), applied to standard models created by Proper
Orthogonal Decomposition (POD) of flows with Galerkin projection. The numerical
analysis of the fully Navier-Stokes discretization for the proposed new POD-ROM
is presented, by mainly deriving the corresponding error estimates. Also, we
suggest an efficient practical implementation of the stabilization term, where
the stabilization parameter is approximated by the Discrete Empirical
Interpolation Method (DEIM).
