A TVD uncertainty quantification method with bounded error applied to transonic airfoil flutter

The Unsteady Adaptive Stochastic Finite Elements (UASFE) approach is a robust and efficient uncertainty quantification method for resolving the effect of random parameters in unsteady simulations. In this paper, it is shown that the underlying Adaptive Stochastic Finite Elements (ASFE) method for steady problems based on Newton-Cotes quadrature...

A posteriori error analysis for stochastic finite element solutions of fluid flows with parametric uncertainties

Accounting for uncertainty in numerical simulations is a growing concern and a great deal of methods have recently been developed, such as the Polynomial Chaos which basically consists in a spectral approximation of the surface response of the solution by stochastic finite elements. However, criteria for refinement of the spectral space have so...