Reduced basis model order reduction in optimal control of a nonsmooth semilinear elliptic PDE

Abstract

In this paper, an optimization problem governed by a nonsmooth semilinear elliptic partial differential equation is considered. A reduced order approach is applied in order to obtain a computationally fast and certified numerical solution approach. Using the reduced basis method and efficient a-posteriori error estimation for the primal and dual equations, an adaptive algorithm is developed and tested successfully for several numerical examples.