Haar-type stochastic Galerkin formulations for hyperbolic systems with Lipschitz continuous flux function

2022/03/22 by Stephan Gerster, Gerster, Stephan, Aleksey Sikstel +3 · 1 citation
Computer Science · Economics, Econometrics and Finance · Engineering · #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Probability (math.PR) #Reservoir Engineering and Simulation Methods #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2203.11718

openalex publication_date 2022/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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