@Article{CiCP-6-406,
author = {Jeroen A. S. Witteveen and Hester Bijl},
title = {A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter},
journal = {Communications in Computational Physics},
year = {2009},
volume = {6},
number = {2},
pages = {406--432},
abstract = {<p style="text-align: justify;">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 in simplex elements is extrema diminishing (ED). It is also
shown that the method is total variation diminishing (TVD) for one random parameter
and for multiple random parameters for first degree Newton-Cotes quadrature. It is
proven that the interpolation of oscillatory samples at constant phase in the UASFE
method for unsteady problems results in a bounded error as function of the phase for
periodic responses and under certain conditions also in a bounded error in time. The
two methods are applied to a steady transonic airfoil flow and a transonic airfoil flutter
problem.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7687.html}
}