A-posteriori error estimation of discrete POD models for PDE-constrained optimal control

Abstract

In this work a-posteriori error estimates for linear-quadratic optimal control problems governed by parabolic equations are considered. Different error estimation techniques for finite element discretizations and model-order reduction are combined to validate suboptimal control solutions from low-order models which are constructed by Galerkin discretization and application of proper orthogonal decomposition (POD). The theoretical findings are used to design an efficient updating algorithm for the reduced-order models; the efficiency and accuracy is illustrated by numerical experiments.