Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations

Julio Castrillon, Fabio Nobile, Raul Tempone

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remapped onto a corresponding PDE with a fixed deterministic domain. We show that the solution can be analytically extended to a well defined region in CN with respect to the random variables. A sparse grid stochastic collocation method is then used to compute the mean and variance of the QoI. Finally, convergence rates for the mean and variance of the QoI are derived and compared to those obtained in numerical experiments.
Original languageEnglish (US)
Pages (from-to)1173-1197
Number of pages25
JournalComputers & Mathematics with Applications
Volume71
Issue number6
DOIs
StatePublished - Mar 2 2016

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