Volume 27, Issue 3
Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations

Stephan Gerster & Michael Herty

Commun. Comput. Phys., 27 (2020), pp. 639-671.

Published online: 2020-02

[An open-access article; the PDF is free to any online user.]

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  • Abstract

Stochastic quantities of interest are expanded in generalized polynomial chaos expansions using stochastic Galerkin methods. An applicationto hyperbolic differential equations does in general 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, wellposedness and energy estimates.

  • Keywords

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

  • AMS Subject Headings

subject classifications: 35L65, 54C70, 58J45, 70S10, 37L45, 35R60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gerster@igpm.rwth-aachen.de (Stephan Gerster)

herty@igpm.rwth-aachen.de (Michael Herty)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-639, author = {Gerster , Stephan and Herty , Michael }, title = {Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {3}, pages = {639--671}, abstract = {

Stochastic quantities of interest are expanded in generalized polynomial chaos expansions using stochastic Galerkin methods. An applicationto hyperbolic differential equations does in general 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, wellposedness and energy estimates.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0047}, url = {http://global-sci.org/intro/article_detail/cicp/13925.html} }
TY - JOUR T1 - Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations AU - Gerster , Stephan AU - Herty , Michael JO - Communications in Computational Physics VL - 3 SP - 639 EP - 671 PY - 2020 DA - 2020/02 SN - 27 DO - http://dor.org/10.4208/cicp.OA-2019-0047 UR - https://global-sci.org/intro/cicp/13925.html KW - Hyperbolic partial differential equations, uncertainty quantification, stochastic Galerkin, shallow water equations, wellposedness, entropy, Roe variable transform. AB -

Stochastic quantities of interest are expanded in generalized polynomial chaos expansions using stochastic Galerkin methods. An applicationto hyperbolic differential equations does in general 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, wellposedness and energy estimates.

Stephan Gerster & Michael Herty. (2020). Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations. Communications in Computational Physics. 27 (3). 639-671. doi:10.4208/cicp.OA-2019-0047
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