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research article

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

Beck, Joakim
•
Nobile, Fabio  
•
Tamellini, Lorenzo  
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2014
Computers and Mathematics with Applications

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.

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Type
research article
DOI
10.1016/j.camwa.2013.03.004
Web of Science ID

WOS:000332751300003

Author(s)
Beck, Joakim
Nobile, Fabio  
Tamellini, Lorenzo  
Tempone, Raul
Date Issued

2014

Published in
Computers and Mathematics with Applications
Volume

67

Issue

4

Start page

732

End page

751

Subjects

Uncertainty Quantification

•

Elliptic PDEs with random data

•

Multivariate polynomial approximation

•

Best M –terms polynomial approximation

•

Stochastic Galerkin method

•

Sub-exponential convergence

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
CSQI  
RelationURL/DOI

IsNewVersionOf

https://infoscience.epfl.ch/record/263084
Available on Infoscience
August 22, 2012
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/84983
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