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Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations

Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations
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Year:    2020

Author:    Stephan Gerster, Michael Herty

Communications in Computational Physics, Vol. 27 (2020), Iss. 3 : pp. 639–671

Abstract

Stochastic quantities of interest are expanded in generalized polynomial chaos expansions using stochastic Galerkin methods. An application of hyperbolic differential equations in general does not transfer hyperbolicity to the coefficients of the truncated series expansion. For the Haar basis and for piecewise linear multiwavelets we present convex entropies for the systems of coefficients of the one-dimensional shallow water equations by using the Roe variable transform. This allows to obtain hyperbolicity, well-posedness and energy estimates.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2019-0047

Communications in Computational Physics, Vol. 27 (2020), Iss. 3 : pp. 639–671

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    33

Keywords:    Hyperbolic partial differential equations uncertainty quantification stochastic Galerkin shallow water equations well-posedness entropy Roe variable transform.

Author Details

Stephan Gerster

Michael Herty

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