Optimality conditions and POD a-posteriori error estimates for a semilinear parabolic optimal control

Abstract

In the present paper the authors consider an optimal control problem for a parametrized nonlinear parabolic differential equation, which is motivated by lithium-ion battery models. A standard finite element (FE) discretization leads to a large-scale nonlinear optimization problem so that its numerical solution is very costly. Therefore, a reduced-order modelling based on proper orthogonal decomposition (POD) is applied, so that the number of degrees of freedom is reduced significantly and a fast numerical simulation of the model is possible. To control the error, an a-posteriori error estimator is realized. Numerical experiments show the efficiency of the approach.