An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
Finite Elements in Analysis and Design
A Spectral Stochastic Semi-Lagrangian Method for Convection-Diffusion Equations with Uncertainty
Journal of Scientific Computing
Linear quadratic regulation of systems with stochastic parameter uncertainties
Automatica (Journal of IFAC)
Uncertainty investigations in nonlinear aeroelastic systems
Journal of Computational and Applied Mathematics
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In this paper, we solve the two-dimensional advection-diffusion equation with random transport velocity. The generalized polynomial chaos expansion is employed to discretize the equation in random space while the spectral hp element method is used for spatial discretization. Numerical results which demonstrate the convergence of generalized polynomial chaos are presented. Specifically, it appears that the fast convergence rate in the variance is the same as that of the mean solution in the Jacobi-chaos unlike the Hermite-chaos. To this end, a new model to represent compact Gaussian distributions is also proposed.