期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 59, 期 4, 页码 2163-2196出版社
SIAM PUBLICATIONS
DOI: 10.1137/20M1371798
关键词
proper orthogonal decomposition; reduced order model; error analysis; optimality
资金
- European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Actions [872442]
- National Science Foundation [DMS-2012253, DMS-1953113, CMMI-1929731, DMS-1439786]
- Spanish MCINYU [RTI2018-093521-B-C31]
- Spanish State Research Agency through the national program Juan de la Cierva-Incorporacion 2017
- Simons Foundation [50736]
This paper resolves long-standing issues regarding optimal error bounds for POD reduced order modeling of the heat equation, showing that using difference quotients can lead to optimal errors in both time and ROM discretization.
In this paper, we resolve several long-standing issues dealing with optimal pointwise in time error bounds for proper orthogonal decomposition (POD) reduced order modeling of the heat equation. In particular, we study the role played by difference quotients (DQs) in obtaining reduced order model (ROM) error bounds that are optimal with respect to both the time discretization error and the ROM discretization error. When the DQs are not used, we prove that both the POD projection error and the ROM error are suboptimal. When the DQs are used, we prove that both the POD projection error and the ROM error are optimal. The numerical results for the heat equation support the theoretical results.
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