Convergence of quasi-optimal Stochastic Galerkin Methods for a class of PDES with random coefficients

30/2012

Convergence of quasi-optimal Stochastic Galerkin Methods for a class of PDES with random coefficients

Thursday 26th July 2012

Beck, J.; Nobile, F.; Tamellini, L.; Tempone, R.;

In this work we consider quasi-optimal versions of the Stochastic Galerkin Method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite 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 C^N. 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 specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates.