In our previous work [J. R. Singler, SIAM J. Numer. Anal., 52 (2014), pp. 852- 876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various POD projections of the data and obtained new results concerning POD projection errors and error bounds for POD reduced order models of PDEs. In this work, we improve on our earlier results concerning POD projections by extending to a more general framework that allows for nonorthogonal POD projections and seminorms. We obtain new exact error formulas and convergence results for POD data approximation errors, and also prove new pointwise convergence results and error bounds for POD projections. We consider both the discrete and continuous cases of POD. We also apply our results to several example problems and show how the new results improve on previous work.


Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Approximation theory; Projections; Proper orthogonal decomposition

International Standard Serial Number (ISSN)

0036-1429; 1095-7170

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2021 Society for Industrial and Applied Mathematics (SIAM), All rights reserved.

Publication Date

10 Nov 2020