Monte-Carlo finite-volume methods in uncertainty quantification for hyperbolic conservation laws (Q1627230)

The paper is a survey of non-intrusive computational methods and their implementation in computational uncertainty quantification for nonlinear hyperbolic conservation laws with random inputs. Sampling methods of Monte Carlo, multi-level Monte Carlo type, and stochastic collocation methods are discussed. Both the Monte Carlo and multi-level Monte Carlo methods are formulated and combined with a finite volume space-time discretization to obtain rigorous convergence rates. Some numerical experiments involving systems of conservation laws are presented to illustrate the robustness of the multi-level Monte Carlo methods and its comparison with the Monte Carlo method. For the entire collection see [Zbl 1393.35003].