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

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 DG solution using multiwavelets defined on hierarchy nested grids. Typically this applied dyadic grid hierarchies where explicit construction be performed only one reference element. For non-uniform have constructed each element and, thus, becomes extremely expensive. To overcome problem developed that avoids multiwavelets.