Adaptive multiresolution discontinuous Galerkin schemes for conservation laws: multi-dimensional case

The concept of multiresolution-based adaptive DG schemes for non-linear one-dimensional hyperbolic conservation laws has been developed and investigated analytically and numerically in (Math Comp, doi: 10.1090/S0025-5718-2013-02732-9 , 2013 ). The key idea is to perform a multiresolution analysis us...

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Bibliographic Details
Published in:Computational and Applied Mathematics 2016-07, Vol.35 (2), p.321-349
Main Authors: Gerhard, Nils, Müller, Siegfried
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
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Summary:The concept of multiresolution-based adaptive DG schemes for non-linear one-dimensional hyperbolic conservation laws has been developed and investigated analytically and numerically in (Math Comp, doi: 10.1090/S0025-5718-2013-02732-9 , 2013 ). The key idea is to perform a multiresolution analysis using multiwavelets on a hierarchy of nested grids for the data given on a uniformly refined mesh. This provides difference information between successive refinement levels that may become negligibly small in regions where the solution is locally smooth. Applying hard thresholding the data are highly compressed and local grid adaptation is triggered by the remaining significant coefficients. The focus of the present work lies on the extension of the originally one-dimensional concept to higher dimensions and the verification of the choice for the threshold value by means of parameter studies performed for linear and non-linear scalar conservation laws.
ISSN:0101-8205
1807-0302
DOI:10.1007/s40314-014-0134-y