A Wavelet-Free Approach for Multiresolution-Based Grid Adaptation for Conservation Laws
- Resource Type
- Academic Journal
- Authors
- Nils Gerhard; Siegfried Müller; Aleksey Sikstel
- Source
- 应用数学与计算数学学报 / Communication on applied mathematics and computation. 4(1):108-142
- Subject
- Discontinuous Galerkin
Grid adaptivity
Multiwavelets
Multiresolution analysis
Conservation laws
- Language
- Chinese
- ISSN
- 1006-6330
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 defined 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.