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

TL;DR

This paper develops an a-priori error estimate for space-time POD model reduction applied to linear parabolic PDEs, providing theoretical bounds and numerical validation.

Contribution

It introduces the first a-priori error estimate for space-time POD, extending standard POD to reduce both space and time dimensions in linear evolution problems.

Findings

Error bounds match numerical results closely.

The method effectively estimates the reduction error in space-time POD.

Numerical examples validate the theoretical error estimates.

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.