This note proves, for simplicity for the heat equation, that using BDF2 as time stepping scheme in POD-ROM methods with snapshots based on difference quotients gives both the optimal second order error bound in time and pointwise estimates.

翻译：本文以热方程为例，证明了在基于差商快照的POD-ROM方法中，使用BDF2时间推进格式可同时获得时间方向上的最优二阶误差界与逐点估计。