A Priori Error Bounds for POD-ROMs for Fluids: A Brief Survey
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916377233719296 |
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| author | Ballarin, Francesco Iliescu, Traian |
| author_facet | Ballarin, Francesco Iliescu, Traian |
| contents | Galerkin reduced order models (ROMs), e.g., based on proper orthogonal decomposition (POD) or reduced basis methods, have achieved significant success in the numerical simulation of fluid flows. The ROM numerical analysis, however, is still being developed. In this paper, we take a step in this direction and present a survey of a priori error bounds, with a particular focus on POD-based ROMs. Specifically, we outline the main components of ROM a priori error bounds, emphasize their practical importance, and discuss significant contributions to a priori error bounds for ROMs for fluids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00621 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Priori Error Bounds for POD-ROMs for Fluids: A Brief Survey Ballarin, Francesco Iliescu, Traian Numerical Analysis Fluid Dynamics Galerkin reduced order models (ROMs), e.g., based on proper orthogonal decomposition (POD) or reduced basis methods, have achieved significant success in the numerical simulation of fluid flows. The ROM numerical analysis, however, is still being developed. In this paper, we take a step in this direction and present a survey of a priori error bounds, with a particular focus on POD-based ROMs. Specifically, we outline the main components of ROM a priori error bounds, emphasize their practical importance, and discuss significant contributions to a priori error bounds for ROMs for fluids. |
| title | A Priori Error Bounds for POD-ROMs for Fluids: A Brief Survey |
| topic | Numerical Analysis Fluid Dynamics |
| url | https://arxiv.org/abs/2409.00621 |