Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations

Authors

  • Stephan Gerster RWTH Aachen, Institut fu¨r Geometrie und Praktische Mathematik, Templergraben 55, 52062 Aachen, Germany.
  • Michael Herty RWTH Aachen, Institut fu¨r Geometrie und Praktische Mathematik, Templergraben 55, 52062 Aachen, Germany.

DOI:

https://doi.org/10.4208/cicp.OA-2019-0047

Keywords:

Hyperbolic partial differential equations, uncertainty quantification, stochastic Galerkin, shallow water equations, well-posedness, entropy, Roe variable transform.

Abstract

Stochastic quantities of interest are expanded in generalized polynomial chaos expansions using stochastic Galerkin methods. An application of hyperbolic differential equations in general does 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.

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Published

2020-07-30

Issue

Vol. 27 No. 3 (2020)

Section

Articles