In this line of research we consider the case in which the uncertainty can be described reasonably well in a probabilistic setting and we focus on the problem of effectively propagating it from the input parameters to the output quantities of interest of the mathematical model. In particular we focus on non-intrusive numerical methods that imply solving the problem for a well chosen set of input parameters and make inference on the statistical properties of the output quantities based on the corresponding evaluations.
J. Back, F. Nobile, L. Tamellini and R. Tempone,Stochastic Spectral Galerkin and collocation methods for PDEs with random coefficients: a numerical comparison. Spectral and High Order Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering, Volume 76, 43-62, 2011.