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Convergence of quasi-optimal stochastic Galerkin methods for a class of PDEs with random coefficients

Bibliography:

J. Beck, F. Nobile, L. Tamellini, R. Tempone,  Convergence of quasi-optimal stochastic Galerkin methods for a class of PDEs with random coefficientsComputers & Mathematics with Applications. Volume 67, Issue 4, March 2014, Pages 732–751.

Authors:

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

Keywords:

Uncertainty Quanti

Year:

2014

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 speci c application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates.

ISSN:

DOI information: 10.1016/j.camwa.2013.03.004.