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.
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.