488
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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 |