TY - EJOUR
DO - 10.1016/j.camwa.2016.01.005
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 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.
T1 - Analytic regularity and collocation approximation for elliptic PDEs with Random domain deformations
IS - 6
DA - 2016
AU - Castrillón-Candás, Julio Enrique
AU - Nobile, Fabio
AU - Tempone, Raúl
JF - Computers and Mathematics with Applications
SP - 1173-1197
VL - 71
EP - 1173-1197
ID - 200022
KW - Uncertainty Quantification
KW - Stochastic Collocation
KW - Stochastic PDEs
KW - Finite Elements
KW - Complex Analysis
KW - Smolyak Sparse Grids
SN - 0898-1221
UR - http://infoscience.epfl.ch/record/200022/files/2016_Castrillon_Nobile_Tempone_CAMWA_RandomDom.pdf
ER -