A Wavelet-Free Approach for Multiresolution-Based Grid Adaptation for Conservation Laws

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  • Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, Aachen 52056, Germany

Received date: 2020-06-22

  Revised date: 2020-11-03

  Online published: 2022-03-01

Abstract

In recent years the concept of multiresolution-based adaptive discontinuous Galerkin (DG) schemes for hyperbolic conservation laws has been developed. The key idea is to perform a multiresolution analysis of the DG solution using multiwavelets defned on a hierarchy of nested grids. Typically this concept is applied to dyadic grid hierarchies where the explicit construction of the multiwavelets has to be performed only for one reference element. For non-uniform grid hierarchies multiwavelets have to be constructed for each element and, thus, becomes extremely expensive. To overcome this problem a multiresolution analysis is developed that avoids the explicit construction of multiwavelets.

Cite this article

Nils Gerhard, Siegfried Müller, Aleksey Sikstel . A Wavelet-Free Approach for Multiresolution-Based Grid Adaptation for Conservation Laws[J]. Communications on Applied Mathematics and Computation, 2022 , 4(1) : 108 -142 . DOI: 10.1007/s42967-020-00101-6

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