TY - JOUR
T1 - Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations
AU - Gerster , Stephan
AU - Herty , Michael
JO - Communications in Computational Physics
VL - 3
SP - 639
EP - 671
PY - 2020
DA - 2020/02
SN - 27
DO - http://doi.org/10.4208/cicp.OA-2019-0047
UR - https://global-sci.org/intro/article_detail/cicp/13925.html
KW - Hyperbolic partial differential equations, uncertainty quantification, stochastic Galerkin, shallow water equations, well-posedness, entropy, Roe variable transform.
AB - <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>