Abstract
In this paper we present an a posteriori error estimate for a reduced order model (ROM) for the incompressible Navier-Stokes equations that is based on the fact that the full order model is a finite element (FE) approximation. Both this FE approximation and the ROM are stabilized by means of a variational multi-scale (VMS) strategy, in which the unknowns are split into FE scales and sub-grid scales (SGS), the latter being modeled in terms of the former. The SGS, when properly scaled, provide directly the a posteriori error estimate, both for the ROM and for the FE approximation.
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