A third order hierarchical basis WENO interpolation for sparse grids with application to conservation laws with uncertain data

Kolb, Oliver

DOI: https://doi.org/10.1007/s10915-017-0503-y
URL: https://link.springer.com/article/10.1007/s10915-0...
Additional URL: https://www.researchgate.net/publication/318548796...
Document Type: Article
Year of publication: 2018
The title of a journal, publication series: Journal of Scientific Computing
Volume: 74
Issue number: 3
Page range: 1480-1503
Place of publication: New York, NY [u.a.]
Publishing house: Springer Science + Business Media B.V.
ISSN: 0885-7474 , 1573-7691
Publication language: English
Institution: School of Business Informatics and Mathematics > Angewandte Mathematik (Juniorprofessur) (Kolb 2012-2021)
Subject: 510 Mathematics
Abstract: In this paper, we introduce a third order hierarchical basis WENO interpolation, which possesses similar accuracy and stability properties as usual WENO interpolations. The main motivation for the hierarchical approach is the direct applicability on sparse grids. This is for instance of large practical interest in the numerical solution of conservation laws with uncertain data, where discontinuities in the physical domain often carry over to the (potentially high-dimensional) stochastic domain. For this, we apply the introduced hierarchical basis WENO interpolation within a non-intrusive collocation method and present first results on 2- and 3-dimensional sparse grids.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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