Long-Term Behavior of Polynomial Chaos in Stochastic Flow Simulations

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An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009, methodology): “The multi-element generalized polynomial chaos method (MEgPC ) was introduced to address discontinuities in the random space while preserving the convergence rate of the gPC method [18] [19] [20].”
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006, background): “The long-term behavior of gPC and ME-gPC was studied in [ 29 ].”
Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed (2010, background): “Wan and Karniadakis had a paper discussing such an issue [12].”
Modeling physical uncertainties in dynamic stall induced fluid-structure interaction of turbine blades using arbitrary polynomial chaos (2007, methodology): “Generalized polynomial chaos and multi-element generalized polynomial chaos have been applied by Karniadakis and co-workers to for example flow problems and fluid–structure interaction problems in [28–31].”
Fast Numerical Methods for Stochastic Computations: A Review (2009, background): “The convergence of gPC for such functions was discussed in [31, 81].”