Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Uncertainty analysis for the steady-state flows in a dual throat nozzle
Journal of Computational Physics
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Predicting shock dynamics in the presence of uncertainties
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Uncertainty quantification for systems of conservation laws
Journal of Computational Physics
Polynomial chaos for simulating random volatilities
Mathematics and Computers in Simulation
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
Journal of Computational Physics
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Numerical Methods for Stochastic Computations: A Spectral Method Approach
Spectral Methods for Parameterized Matrix Equations
SIAM Journal on Matrix Analysis and Applications
Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations
Journal of Computational and Applied Mathematics
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Mathematical modelling of dynamical systems often yields partial differential equations (PDEs) in time and space, which represent a conservation law possibly including a source term. Uncertainties in physical parameters can be described by random variables. To resolve the stochastic model, the Galerkin technique of the generalised polynomial chaos results in a larger coupled system of PDEs. We consider a certain class of linear systems of conservation laws, which exhibit a hyperbolic structure. Accordingly, we analyse the hyperbolicity of the corresponding coupled system of linear conservation laws from the polynomial chaos. Numerical results of two illustrative examples are presented.