Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations (Communications in Computational Physics, 2020)
Stochastic quantities of interest are expanded in generalized polynomialchaos expansions using stochastic Galerkin methods. An application of hyperbolic differential equations in general does not transfer hyperbolicity to the coefficients of thetruncated series expansion. For the Haar basis and for piecewise linear multiwaveletswe present convex entropies for the systems of coefficients of the one-dimensionalshallow water equations by using the Roe variable transform. This allows to obtainhyperbolicity, well-posedness and energy estimates.