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.
Ballarin, F., Iliescu, T., A Priori Error Bounds for POD-ROMs for Fluids: A Brief Survey, in Giacomini, M., Perotto, S., Rozza, G., Emerging Technologies in Computational Sciences for Industry, Sustainability and Innovation, Springer, Cham 2025 <<LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING>>,: 305-320. 10.1007/978-3-031-95709-3_19 [https://hdl.handle.net/10807/325916]
A Priori Error Bounds for POD-ROMs for Fluids: A Brief Survey
Ballarin, Francesco;
2025
Abstract
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.
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