A Third Order Hierarchical Basis WENO Interpolation for Sparse Grids with Application to Conservation Laws with Uncertain Data

A Third Order Hierarchical Basis WENO Interpolation for Sparse Grids with Application to... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

A Third Order Hierarchical Basis WENO Interpolation for Sparse Grids with Application to Conservation Laws with Uncertain Data

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-017-0503-y
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Scientific ComputingSpringer Journals

Published: Jul 19, 2017

References

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