Abstract Due to recent advances in the development of efficient uncertainty quantification methods, the propagation of physical randomness in practical applications has be- come feasible for smooth and steady computational problems. The current challenges in modeling physical variability include problems with unsteadiness and discontinu- ous solutions. In this paper two efficient non-intrusive approaches for unsteady prob- lems are developed based on time-independent parametrization and interpolation at constant phase. The interpolation of the samples is performed using both a global polynomial interpolation and a robust Adaptive Stochastic Finite Elements formula- tion with Newton-Cotes quadrature in simplex elements. Applications to an elastically mounted cylinder, a transonic airfoil flow, and an elastically mounted airfoil illustrate the efficiency, robustness, and straightforward implementation of the methodologies. Keywords: uncertainty quantification, stochastic finite elements, fluid dynamics, fluid- structure interaction, unsteady problems, shock waves, asymptotic behavior, limit cy- cle oscillations, random parameters. 1 Introduction Since the invention of the first modern computers in the mid-20th century, compu- tational resources have increased by many orders of magnitude due to advances in processor clock rate and memory storage. At the same time, the efficiency of numer- ical algorithms has improved by even a larger factor. Numerical errors in industrial simulations, therefore, start to reach acceptable engineering levels. Nowadays, physi- cal variability tends to dominate the error in numerical predictions. Inherent physical variations are caused by for example varying atmospheric conditions, and produc- 1 Paper 16 Unsteady Adaptive Stochastic Finite Elements for Quantification of Uncertainty in Time-Dependent Simulations J.A.S. Witteveen and H. Bijl Faculty of Aerospace Engineering Delft University of Technology, The Netherlands ©Civil-Comp Press, 2008 Proceedings of the Sixth International Conference on Engineering Computational Technology, M. Papadrakakis and B.H.V. Topping, (Editors), Civil-Comp Press, Stirlingshire, Scotland