  In this paper, we propose an efficient proper orthogonal decomposition based
reduced-order model(POD-ROM) for nonstationary Stokes equations, which combines
the classical projection method with POD technique. This new scheme mainly owns
two advantages: the first one is low computational costs since the classical
projection method decouples the reduced-order velocity variable and
reduced-order pressure variable, and POD technique further improves the
computational efficiency; the second advantage consists of circumventing the
verification of classical LBB/inf-sup condition for mixed POD spaces with the
help of pressure stabilized Petrov-Galerkin(PSPG)-type projection method, where
the pressure stabilization term is inherent which allows the use of non inf-sup
stable elements without adding extra stabilization terms. We first obtain the
convergence of PSPG-type finite element projection scheme, and then analyze the
proposed projection POD-ROM's stability and convergence. Numerical experiments
validate out theoretical results.
