  We investigate numerical behaviour of a convection diffusion equation with
random coefficients by approximating statistical moments of the solution.
Stochastic Galerkin approach, turning the original stochastic problem to a
system of deterministic convection diffusion equations, is used to handle the
stochastic domain in this study, whereas discontinuous Galerkin method is used
to discretize spatial domain due to its local mass conservativity. A priori
error estimates of the stationary problem and stability estimate of the
unsteady model problem are derived in the energy norm. To address the curse of
dimensionality of Stochastic Galerkin method, we take advantage of the
low--rank Krylov subspace methods, which reduce both the storage requirements
and the computational complexity by exploiting a Kronecker--product structure
of system matrices. The efficiency of the proposed methodology is illustrated
by numerical experiments on the benchmark problems.

Numerical Analysis;Numerical Analysis