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arXiv · 2604.22057

A-priori error estimation for space-time Galerkin POD for linear evolution problems

Carmen Gräßle·Jan Heiland·Jannis Marquardt
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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.

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BibTeXRIS

Carmen Gräßle, Jan Heiland, Jannis Marquardt. 2026-04-23. A-priori error estimation for space-time Galerkin POD for linear evolution problems. https://arxiv.org/abs/2604.22057

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