Comparison of the reduced-basis and POD a posteriori error estimators for an elliptic linear-quadratic optimal control problem

In this article, a linear-quadratic optimal control problem governed by the Helmholtz equation is considered. For the computation of suboptimal solutions, two different model reduction techniques are compared: the reduced-basis method and proper orthogonal decomposition. By an a posteriori error estimator for the optimal control problem, the accuracy of the suboptimal solutions is ensured. The efficiency of both model reduction approaches is illustrated by a numerical example for the stationary Helmholtz equation.