An adaptive multi-element generalized polynomial chaos method for stochastic differential equations

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

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

Numerical Analysis, Engineering, Orthogonal Polynomials +10

The Homogeneous Chaos

Norbert Wiener · American Journal of Mathematics · 1938 · 3K citations

Chaos Theory, Entropy, High-dimensional Chaos +2

Modeling uncertainty in flow simulations via generalized polynomial chaos

Dongbin Xiu, George Em Karniadakis · Journal of Computational Physics · 2003 · 1.4K citations

Engineering, Chaos Theory, Uncertainty Quantification +5

The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals

R. H. Cameron, W. T. Martin · Annals of Mathematics · 1947 · 1.3K citations

Spectral/hp element methods for CFD

Computers & Mathematics with Applications · 1999 · 673 citations

Numerical Analysis, Finite Element Method, Numerical Computation +7