A stochastic Galerkin method for optimal Dirichlet boundary control problems with uncertain data

Abstract

The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error estimates are derived for the control variable in $L^2(\partial \mathcal{D})$-norm and state variable in $L^2(\hat{I}\text{c◯}\times \mathcal{D})$-norm. To solve large linear systems, appropriate preconditioners are proposed for both unconstrained and constrained scenarios. To illustrate the validity and efficiency of the proposed approaches, some numerical experiments are performed.

28 pages, 5 figures