| 488 | IGPM488.pdf January 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 |
| DOI | 10.4208/cicp.OA-2019-0047 |
| PUBLICATION | Communications in Computational Physics 2020, volume 27, pp 639-671 |
