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.

中文翻译：

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用于不可压缩流的 POD-ROM，包括全阶解的时间导数的快照：压力的误差界限

研究了基于适当正交分解 (POD) 的不可压缩纳维-斯托克斯方程的降阶方法 (ROM)，其中包括从全阶混合有限元方法 (FOM) 逼近速度的时间导数的快照。此外，该组快照包含 FOM 的平均速度。FOM 和 POD-ROM 都配备了梯度稳定功能。该方法的速度误差分析已经可以在文献中找到。本文研究了两种不同的程序来计算压力的近似值，并证明了与粘度的倒数幂无关的压力误差范围。数值研究支持了分析结果并比较了两种方法。