Multiresolution-analysis for stochastic hyperbolic conservation laws

TL;DR

This paper introduces a multiresolution analysis and an adaptive discontinuous Galerkin solver for stochastic hyperbolic conservation laws, significantly improving computational efficiency for complex stochastic distributions.

Contribution

It presents a novel adaptive strategy combined with multiresolution analysis for DG methods applied to stochastic conservation laws, enhancing performance and efficiency.

Findings

Significant performance improvement with the adaptive strategy

Validated efficiency gains through computational experiments

Effective handling of general stochastic distributions

Abstract

A multiresolution analysis for solving stochastic conservation laws is proposed. Using a novel adaptation strategy and a higher dimensional deterministic problem, a discontinuous Galerkin (DG) solver is derived. A multiresolution analysis of the DG spaces for the proposed adaptation strategy is presented. Numerical results show that in the case of general stochastic distributions the performance of the DG solver is significantly improved by the novel adaptive strategy. The gain in efficiency is validated in computational experiments.