A Priori Error Bounds for POD-ROMs for Fluids: A Brief Survey
Numerical Analysis
2024-09-04 v1 Numerical Analysis
Fluid Dynamics
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.
Keywords
Cite
@article{arxiv.2409.00621,
title = {A Priori Error Bounds for POD-ROMs for Fluids: A Brief Survey},
author = {Francesco Ballarin and Traian Iliescu},
journal= {arXiv preprint arXiv:2409.00621},
year = {2024}
}