MLMC Methods for stochastic hyperbolic problems
Please login to view abstract download link
Monte-Carlo (MC) methods are an easy and non-intrusive approach for solving hyperbolic conservation laws with stochastic influence. Their downside is their slow convergence behavior. Multi-level Monte-Carlo (MLMC) methods have the potential to behave in certain situations asymptotically the same in terms of accuracy vs. work as a single deterministic solve. However, for MLMC methods, it is non-trivial whether or whether not structure-preserving properties of the approximate solutions to the deterministic sub-problems transfer to the approximate stochastic solution. In this presentation, we will share our initial findings concerning this question. We will focus on the case of scalar conservation laws and discontinuous stochastic fields. We will consider MLMC methods that employ deterministic methods of varying order. We will provide theoretical considerations as well as numerical results to support our claims.
