Castrillón-Candás, Julio Enrique
Nobile, Fabio
Tempone, Raúl
Analytic regularity and collocation approximation for elliptic PDEs with Random domain deformations
Computers and Mathematics with Applications
Computers and Mathematics with Applications
Computers and Mathematics with Applications
Computers and Mathematics with Applications
25
71
6
Uncertainty Quantification
Stochastic Collocation
Stochastic PDEs
Finite Elements
Complex Analysis
Smolyak Sparse Grids
2016
2016
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.
0898-1221
Computers and Mathematics with Applications
Journal Articles
10.1016/j.camwa.2016.01.005