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.

翻译：在本文中,我们建议对非静止斯托克斯方程式采用高效的正正向分解模型(POD-ROM),将古典投影法与POD技术相结合。这一新方案主要具有两个优点:第一是计算成本低,因为古典投影法分离了降序速度变量和降序压力变量,而POD技术进一步提高了计算效率;第二个好处是,在压力稳定式Petrov-Galerkin(PPPGG)型投影法的帮助下,绕过对混合POD空间传统LBB/in-in-sup条件的核查,而压力稳定式投影法则是内在的,允许使用非内向稳定元素,而不增加额外稳定条件。我们首先获得PSPG-型定式元素预测方案的趋同,然后分析拟议的预测POD-ROD-ROM的稳定性和趋同性。Numerical实验证实了理论结果。