Stochastic collocation for optimal control problems with stochastic PDE constraints by meshless techniques?

In this paper, we investigate the stochastic collocation method with meshless techniques for an optimal control problem of elliptic equations with random inputs. The proposed method does not depend on the mesh partition and only requires the solution of uncoupled deterministic problem at each interpolation point, which can be competitive for high-dimensional random inputs and handle easily a wider range of situations such as random variables that are unbounded and input data that depend nonlinearly on the random variables. A priori error estimates are provided for the control, state and co-state variables. The stochastic collocation method based on gradient projection is presented, and some numerical examples are carried out to illustrate the performance of the new scheme.& COPY; 2023 Elsevier Inc. All rights reserved.