Haar-type stochastic Galerkin formulations for hyperbolic systems with Lipschitz continuous flux function
Numerical Analysis
2025-09-09 v2 Numerical Analysis
Probability
Abstract
This work is devoted to the Galerkin projection of highly nonlinear random quantities. The dependency on a random input is described by Haar-type wavelet systems. The classical Haar sequence has been used by Pettersson, Iaccarino, Nordstroem (2014) for a hyperbolic stochastic Galerkin formulation of the one-dimensional Euler equations. This work generalizes their approach to several multi-dimensional systems with Lipschitz continuous and non-polynomial flux functions. Theoretical results are illustrated numerically by a genuinely multidimensional CWENO reconstruction.
Cite
@article{arxiv.2203.11718,
title = {Haar-type stochastic Galerkin formulations for hyperbolic systems with Lipschitz continuous flux function},
author = {Stephan Gerster and Aleksey Sikstel and Giuseppe Visconti},
journal= {arXiv preprint arXiv:2203.11718},
year = {2025}
}