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

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 C^N 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.


Published in:
Computers and Mathematics with Applications, 71, 6, 1173-1197
Year:
2016
Publisher:
Oxford, Elsevier
ISSN:
0898-1221
Keywords:
Laboratories:


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 Record created 2014-06-25, last modified 2018-10-01

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