An iterative proper orthogonal decomposition method for a parabolic optimal control problem

An iterative proper orthogonal decomposition (POD) method for a parabolic optimal control problem is investigated in this paper. Firstly, we construct the finite element method, where piecewise linear continuous functions are used for space discretization, and the backward Euler method is used for time discretization. Secondly, we apply the POD method as a model order reduction method to reduce the computation. The different POD basis functions for the state and co-state variables are established by an iterative procedure, which takes the finite element solutions at some time instances as snapshots. A priori error estimates are derived for the state, co-state and control variables, respectively. Finally, numerical experiments are provided to support our theoretical results.

Automated summary

This paper investigates an iterative proper orthogonal decomposition (POD) method for a parabolic optimal control problem. The finite element method is constructed, with piecewise linear continuous functions used for space discretization and the backward Euler method used for time discretization. The POD method is then applied as a model order reduction method to reduce computation. Different POD basis functions for the state and co-state variables are established through an iterative procedure, using finite element solutions at certain time instances as snapshots. A priori error estimates are derived for the state, co-state, and control variables. Numerical experiments are provided to support the theoretical results.