Abstract

In this work we consider quasi-optimal versions of the Stochastic
Galerkin Method for solving linear elliptic PDEs with stochastic
coeffcients. In particular, we consider the case of a nite number N of
random inputs and an analytic dependence of the solution of the PDE with
respect to the parameters in a polydisc of the complex plane CN. We
show that a quasi-optimal approximation is given by a Galerkin
projection on a weighted (anisotropic) total degree space and prove a
(sub)exponential convergence rate. As a specic application we consider a
thermal conduction problem with non-overlapping inclusions of random
conductivity. Numerical results show the sharpness of our estimates.