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 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.

Radially symmetric solutions of the ultra-relativistic Euler equations

“…By means of the thresholded sequence a new, locally refined grid is determined. Details on this concept can be found in [11,8,9,10].…”

A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

“…where ρ denotes the density, q = ρv the momentum and p(ρ) = Cρ γ the pressure with C = 1 and γ = 7 5 . We consider two Riemann problems: one where the solution consists of two rarefaction waves and one where we have a rarefaction and a shock.…”

“…For the shock detection we employ the Daubechies wavelets and set the minimal surge strength to σ = 0.1. The error estimator is implemented in the multiwaveframework [7]. The p-system: two rarefactions.…”