488 IGPM488.pdf        2019
TITLE Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations
AUTHORS Stephan Gerster, Michael Herty
ABSTRACT Stochastic quantities of interest are expanded in generalized polynomial chaos expansions using stochastic Galerkin methods. When applied to hyperbolic differential equations, the coefficients of the series do not inherit hyperbolicity in general. Here, we present convex entropies for the systems of coefficients for Burgers’ and shallow water equations. This allows to obtain hyperbolicity, wellposedness and energy estimates.
KEYWORDS Hyperbolic Partial Differential Equations, Uncertainty Quantification, Stochastic Galerkin, Shallow Water Equations, Wellposedness, Entropy