The Department of Scientific Computing at Florida State University presents HYUNG-CHUN LEE Director, Center for Applied Analysis and Scientific Computations Professor, Department of Mathematics Ajou University, Korea "A sparse collocation method for an optimal control problem of SPDE" Thursday, January 31, 2013 3:30 P.M. 499 Dirac Science Library

### Abstract

In this talk, we propose and analyze a stochastic collocation method for solving optimal control problems for elliptic partial differential equations with random coefficients and forcing terms. These input data are assumed to depend on a finite number of random variables. We prove existence of optimal solution and derive an optimality system. In the method, we use a Galerkin approximation in space and a sparse grid collocation in the probability space. We provide error estimates for fully discrete solution using an appropriate norm and analyze the computational efficiency. Computational evidence complements the present theory and shows the effectiveness of the sparse grid stochastic collocation method.