Generalised polynomial chaos for a class of linear conservation laws

DOI10.1007/s10915-011-9511-5zbMath1258.65008OpenAlexW2036917625MaRDI QIDQ2276411

Dongbin Xiu, Roland Pulch

Publication date: 5 November 2012

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-011-9511-5

zbMATH Keywords

Galerkin methodwave equationconservation lawsnumerical examplesshallow water equationshyperbolic systemrandom parametergeneralised polynomial chaos

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

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Cites Work

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• Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
• Uncertainty quantification for systems of conservation laws
• Polynomial chaos for simulating random volatilities
• Uncertainty analysis for the steady-state flows in a dual throat nozzle
• Predicting shock dynamics in the presence of uncertainties
• Spectral Methods for Parameterized Matrix Equations
• POLYNOMIAL CHAOS FOR LINEAR DIFFERENTIAL ALGEBRAIC EQUATIONS WITH RANDOM PARAMETERS
• Polynomial chaos for the approximation of uncertainties: Chances and limits
• Finite Volume Methods for Hyperbolic Problems
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• High-Order Collocation Methods for Differential Equations with Random Inputs

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