@Article{CiCP-27-639,
author = {Gerster , Stephan and Herty , Michael},
title = {Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations},
journal = {Communications in Computational Physics},
year = {2020},
volume = {27},
number = {3},
pages = {639--671},
abstract = {<p style="text-align: justify;">Stochastic quantities of interest are expanded in generalized polynomial
chaos expansions using stochastic Galerkin methods. An application of hyperbolic differential equations in general <span style="text-align: justify;">does&nbsp;</span>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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2019-0047},
url = {http://global-sci.org/intro/article_detail/cicp/13925.html}
}