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

Joakim Beck, Fabio Nobile, Lorenzo Tamellini, Raul Tempone

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

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 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. © 2013 Elsevier Ltd. All rights reserved.
Original languageEnglish (US)
Pages (from-to)732-751
Number of pages20
JournalComputers & Mathematics with Applications
Volume67
Issue number4
DOIs
StatePublished - Mar 2014

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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