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Erschienen in:
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2017 | OriginalPaper | Buchkapitel

The Stochastic Finite Volume Method

verfasst von : Rémi Abgrall, Svetlana Tokareva

Erschienen in: Uncertainty Quantification for Hyperbolic and Kinetic Equations

Verlag: Springer International Publishing

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Abstract

We give the general principle of the Stochastic Finite Volume method and show its versatility by many examples from standard ODE to fluid problems. We derive the error estimates for the mean and variance resulting from the SFVM and show that the convergence rates of the statistical quantities are equivalent to the convergence rates of the deterministic solution. We propose the anisotropic choice of the mesh nodes for high-dimensional stochastic parameter spaces and analyze the efficiency of the anisotropic stochastic mesh adaptation algorithm.
We finally generalize the SFVM approach and apply the DG discretization on the unstructured triangular grids in the physical space. We demonstrate the efficiency and the scaling of the implemented methods on various numerical tests.

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Nächstes Kapitel Uncertainty Modeling and Propagation in Linear Kinetic Equations
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Metadaten
Titel
The Stochastic Finite Volume Method
verfasst von
Rémi Abgrall
Svetlana Tokareva
Copyright-Jahr
2017
Buch
Uncertainty Quantification for Hyperbolic and Kinetic Equations

Print ISBN: 978-3-319-67109-3

Electronic ISBN: 978-3-319-67110-9

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-67110-9_1