Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

Dongbin Xiu, George Em Karniadakis · SIAM Journal on Scientific Computing · 2002 · 4.7K citations

Natural Sciences, Computational Engineering, Mathematics +16

High-Order Collocation Methods for Differential Equations with Random Inputs

Dongbin Xiu, Jan S. Hesthaven · SIAM Journal on Scientific Computing · 2005 · 1.5K citations · Full text

Computing, Computational Engineering, Finite Element Analysis +15

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

Ivo Babuška, Fabio Nobile, Raúl Tempone · SIAM Journal on Numerical Analysis · 2007 · 1.4K citations · Full text

Computing, Computational Engineering, Probability Theory +16

The stochastic finite element method: Past, present and future

George Stefanou · Computer Methods in Applied Mechanics and Engineering · 2008 · 977 citations · Full text

Computing, Computational Engineering, Mechanical Engineering +12

A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

Fabio Nobile, Raúl Tempone, Clayton Webster · SIAM Journal on Numerical Analysis · 2008 · 950 citations · Full text

Computing, Computational Engineering, Finite Element Analysis +13