A third order hierarchical basis WENO interpolation for sparse grids with application to conservation laws with uncertain data (Q1743427)
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scientific article; zbMATH DE number 6859532
| Language | Label | Description | Also known as |
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| English | A third order hierarchical basis WENO interpolation for sparse grids with application to conservation laws with uncertain data |
scientific article; zbMATH DE number 6859532 |
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A third order hierarchical basis WENO interpolation for sparse grids with application to conservation laws with uncertain data (English)
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13 April 2018
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The author considers a weighted essentially non-oscillatory (WENO) scheme to solve hyperbolic PDEs that may involve uncertain data. He introduces a third-order hierarchical basis WENO interpolation (HB-WENO) which can be applied for stochastic collocation methods on sparse grids. He proves the usual accuracy and stability properties of the method and shows a third-order accuracy in smooth regions, and second-order accuracy arbitrarily close to the discontinuities. Theoretical results are validated with numerical computations.
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(WENO) weighted essentially non-oscillatory interpolation
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sparse grid
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uncertainty quantification
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