Artículo
On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal
Autor/es | Koc, Birgul
Rubino, Samuele Schneier, Michael Singler, John Iliescu, Traian |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2021-08-05 |
Fecha de depósito | 2022-12-12 |
Publicado en |
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Resumen | In this paper, we resolve several long-standing issues dealing with optimal pointwisein time error bounds for proper orthogonal decomposition (POD) reduced order modeling of the heatequation. In particular, we study the ... In this paper, we resolve several long-standing issues dealing with optimal pointwisein time error bounds for proper orthogonal decomposition (POD) reduced order modeling of the heatequation. In particular, we study the role played by difference quotients (DQs) in obtaining reducedorder model (ROM) error bounds that are optimal with respect to both the time discretizationerror and the ROM discretization error. When the DQs are not used, we prove that both the PODprojection error and the ROM error are suboptimal. When the DQs are used, we prove that both thePOD projection error and the ROM error are optimal. The numerical results for the heat equationsupport the theoretical results. |
Cita | Koc, B., Rubino, S., Schneier, M., Singler, J. y Iliescu, T. (2021). On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal. SIAM journal on numerical analysis, 59 (4), 2163-2196. https://doi.org/10.1137/20M1371798. |
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