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Uncertainty Quantification for Hyperbolic Systems of Conservation Laws


Abgrall, R; Mishra, S (2017). Uncertainty Quantification for Hyperbolic Systems of Conservation Laws. Handbook of Numerical Analysis, 18:507-544.

Abstract

We review uncertainty quantification (UQ) for hyperbolic systems of conservation (balance) laws. The input uncertainty could be in the initial data, fluxes, coefficients, source terms or boundary conditions. We focus on forward UQ or uncertainty propagation and review deterministic methods such as stochastic Galerkin and stochastic collocation finite volume methods for approximating random (field) entropy solutions. Statistical sampling methods of the Monte Carlo and multilevel Monte Carlo (MLMC) type are also described. We present alternative UQ frameworks such as measure-valued solutions and statistical solutions. © 2017 Elsevier B.V.

Abstract

We review uncertainty quantification (UQ) for hyperbolic systems of conservation (balance) laws. The input uncertainty could be in the initial data, fluxes, coefficients, source terms or boundary conditions. We focus on forward UQ or uncertainty propagation and review deterministic methods such as stochastic Galerkin and stochastic collocation finite volume methods for approximating random (field) entropy solutions. Statistical sampling methods of the Monte Carlo and multilevel Monte Carlo (MLMC) type are also described. We present alternative UQ frameworks such as measure-valued solutions and statistical solutions. © 2017 Elsevier B.V.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:October 2017
Deposited On:05 Oct 2017 10:37
Last Modified:06 Oct 2017 07:34
Publisher:Elsevier
ISSN:1570-8659
ISBN:9780444639103
Publisher DOI:https://doi.org/10.1016/bs.hna.2016.11.003

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