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

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.


Published in:
Computers and Mathematics with Applications, 67, 4, 732–751
Year:
2014
Publisher:
Oxford, Elsevier
ISSN:
0898-1221
Keywords:
Laboratories:


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 Record created 2012-08-22, last modified 2018-03-13

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