Numerical Analysis of POD A-Posteriori Error Estimation for Optimal Control

Abstract

In this paper a linear-quadratic optimal control problem governed by a parabolic equation is considered. To solve this problem numerically a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The error between the POD suboptimal control and the optimal controlof the original problem is controlled by an a-posteriori error analysis. In this paper the authors focus on testing the a-posteriori error estimate's validity by means of numerical examples. An intensive study of the consequencesof certain choices that can be made within the POD basis determination process is carried out and the findings are discussed.