A new approach to proper orthogonal decomposition with difference quotients

In a recent work (Koc et al., SIAM J. Numer. Anal. 59(4), 2163–2196, 2021), the authors showed that including difference quotients (DQs) is necessary in order to prove optimal pointwise time error bounds for proper orthogonal decomposition (POD) reduced models of heat equation. this work, we introduce new approach DQs POD procedure. Instead computing modes using all snapshot data and DQs, only use first along with special weights. We show retains numerical analysis benefits standard DQ approach, while set has approximately half number snapshots as i.e., requires less computational effort. illustrate our theoretical results experiments.