A-priori error estimation for space-time Galerkin POD for linear evolution problems
Provides theoretical error guarantees for a specific MOR technique, but is incremental as it extends existing POD theory to the space-time setting.
The paper derives an a-priori error estimate for space-time POD model order reduction applied to linear parabolic PDEs, and validates the theoretical bounds with numerical examples.
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.