  We investigate a numerical behaviour of robust deterministic optimal control
problem subject to a convection diffusion equation containing uncertain inputs.
Stochastic Galerkin approach, turning the original optimization problem
containing uncertainties into a large system of deterministic problems, is
applied to discretize the stochastic domain, while a discontinuous Galerkin
method is preferred for the spatial discretization due to its better
convergence behaviour for optimization problems governed by convection
dominated PDEs. Error analysis is done for the state and adjoint variables in
the energy norm, while the estimates of deterministic control is obtained in
the $L^2$--norm. Large matrix system emerging from the stochastic Galerkin
method is addressed by the low--rank version of GMRES method, which reduces
both the computational complexity and the memory requirements by employing
Kronecker--product structure of the obtained linear system. Benchmark examples
with and without control constraints are presented to illustrate the efficiency
of the proposed methodology.
