Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations
KAUST DepartmentApplied Mathematics and Computational Science Program
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Online Publication Date2016-03-02
Print Publication Date2016-03
Embargo End Date2018-03-10
Permanent link to this recordhttp://hdl.handle.net/10754/622174
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AbstractIn 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.
CitationCastrillón-Candás JE, Nobile F, Tempone RF (2016) Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations. Computers & Mathematics with Applications 71: 1173–1197. Available: http://dx.doi.org/10.1016/j.camwa.2016.01.005.