Uncertainty quantification with adaptive mesh refinement in a chemical system

This paper presents an efficient a posteriori error analysis for stochastic PDEs. While adaptive methods have already been used to quantify uncertainty of large scale and/or high dimensional problems, no rigorous criterion for the adaption strategy exists and the different techniques all rely on heuristic considerations. An extension of the dual-based a posteriori error analysis is here presented in the uncertainty quantification framework. The method allows both for refinement and coarsening of the stochastic discretization, leading to an efficient tool. A stiff chemical system with uncertain reactions rates is considered to illustrate the technique. A 8-D uncertain problem arises which solution is intractable without a specific strategy while the present technique is shown to perform well and at a reasonable computational cost.