Home > Publications > Manuscripts > Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations
Publications

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

Bibliography:

J. E. Castrillon-Candas, F. Nobile, R. F. Tempone, Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations, Accepted for publication in Computers and Mathematics with Applications, Jan. 2016

Authors:

J. E. Castrillon-Candas, F. Nobile, R. F. Tempone

Keywords:

Uncertainty Quantification, Stochastic Collocation, Stochastic PDEs, Finite Elements, Complex Analysis, Smolyak Sparse Grids.

Year:

2016

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 on to a corresponding PDE with a fixed deterministic domain. We show that t he 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 standard deviation of the QoI. Finally, convergence rates for the mean and variance of the QoI are derived and compared to those obtained in numerical experiments.

ISSN:

2016