Abstract
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.
Recommended Citation
S. Locke and J. R. Singler, "New Proper Orthogonal Decomposition Approximation Theory for PDE Solution Data," SIAM Journal on Numerical Analysis, vol. 58, no. 6, pp. 3251 - 3285, Society for Industrial and Applied Mathematics (SIAM), Nov 2020.
The definitive version is available at https://doi.org/10.1137/19M1297002
Department(s)
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
text
Language(s)
English
Rights
© 2021 Society for Industrial and Applied Mathematics (SIAM), All rights reserved.
Publication Date
10 Nov 2020
