TY - JOUR

T1 - Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations

AU - Castrillon, Julio

AU - Nobile, Fabio

AU - Tempone, Raul

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2016/3/2

Y1 - 2016/3/2

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/622174

UR - http://arxiv.org/pdf/1312.7845

UR - http://www.scopus.com/inward/record.url?scp=84959893225&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2016.01.005

DO - 10.1016/j.camwa.2016.01.005

M3 - Article

SN - 0898-1221

VL - 71

SP - 1173

EP - 1197

JO - Computers & Mathematics with Applications

JF - Computers & Mathematics with Applications

IS - 6

ER -