Reduced order methods (ROMs) for the incompressible Navier--Stokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the temporal derivative of the velocity from a full order mixed finite element method (FOM). In addition, the set of snapshots contains the mean velocity of the FOM. Both the FOM and the POD-ROM are equipped with a grad-div stabilization. A velocity error analysis for this method can be found already in the literature. The present paper studies two different procedures to compute approximations to the pressure and proves error bounds for the pressure that are independent of inverse powers of the viscosity. Numerical studies support the analytic results and compare both methods.

翻译：基于本征正交分解（POD）的不可压缩纳维-斯托克斯方程降阶方法（ROM）被研究，该方法包含逼近全阶混合有限元方法（FOM）速度时间导数的快照。此外，快照集合包含FOM的平均速度。FOM和POD-ROM均配备了梯度-散度稳定化处理。关于该方法的速度误差分析已在文献中有所报道。本文研究了计算压力近似的两种不同流程，并证明了与黏度负幂次无关的压力误差界。数值实验支持了分析结果，并对两种方法进行了比较。