MATHICSE-GroupBeck, JoakimNobile, FabioTamellini, LorenzoTempone, Raúl2019-01-212019-01-212019-01-212012-07-1310.5075/epfl-MATHICSE-263084https://infoscience.epfl.ch/handle/20.500.14299/153551In 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 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 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 specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates.Uncertainty QuanticationPDEs with random datalinear elliptic equationsmultivariate polynomial approximationbest M -terms polynomial approximationStochastic Galerkin methodtext::working paper