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In this paper, we propose an efficient proper orthogonal decomposition basedreduced-order model(POD-ROM) for nonstationary Stokes equations, which combinesthe classical projection method with POD technique. This new scheme mainly ownstwo advantages: the first one is low computational costs since the classicalprojection method decouples the reduced-order velocity variable andreduced-order pressure variable, and POD technique further improves thecomputational efficiency; the second advantage consists of circumventing theverification of classical LBB/inf-sup condition for mixed POD spaces with thehelp of pressure stabilized Petrov-Galerkin(PSPG)-type projection method, wherethe pressure stabilization term is inherent which allows the use of non inf-supstable elements without adding extra stabilization terms. We first obtain theconvergence of PSPG-type finite element projection scheme, and then analyze theproposed projection POD-ROM's stability and convergence. Numerical experimentsvalidate out theoretical results.

An efficient Chorin-Temam projection proper orthogonal decomposition based reduced-order model for nonstationary Stokes equations