A-priori error estimation for space-time Galerkin POD for linear evolution problems
Numerical Analysis
2026-04-27 v1 Numerical Analysis
Abstract
In this paper, we propose an a-priori error estimate for the model order reduction (MOR) method of space-time proper orthogonal decomposition (space-time POD). The original space-time POD approach extends standard POD by reducing not only the space dimension but simultaneously the time dimension as well. The proposed a-priori error estimate is developed for a linear parabolic partial differential equation and estimates the error between the numerical solution to a linear parabolic partial differential equation (PDE) and its space-time POD reduced solution. Numerical examples illustrate the occurring errors and analyze them in comparison to the theoretical bounds.
Keywords
Cite
@article{arxiv.2604.22057,
title = {A-priori error estimation for space-time Galerkin POD for linear evolution problems},
author = {Carmen Gräßle and Jan Heiland and Jannis Marquardt},
journal= {arXiv preprint arXiv:2604.22057},
year = {2026}
}