@Article{CiCP-28-4,
author = {Schlachter, Louisa and Totzeck, Claudia},
title = {Parameter Identification in Uncertain Scalar Conservation Laws Discretized with the Discontinuous Stochastic Galerkin Scheme},
journal = {Communications in Computational Physics},
year = {2020},
volume = {28},
number = {4},
pages = {1585--1608},
abstract = {<p style="text-align: justify;">We study an identification problem which estimates the parameters of the
underlying random distribution for uncertain scalar conservation laws. The hyperbolic equations are discretized with the so-called discontinuous stochastic Galerkin
method, i.e., using a spatial discontinuous Galerkin scheme and a Multielement stochastic Galerkin ansatz in the random space. We assume an uncertain flux or uncertain
initial conditions and that a data set of an observed solution is given. The uncertainty is assumed to be uniformly distributed on an unknown interval and we focus on
identifying the correct endpoints of this interval. The first-order optimality conditions
from the discontinuous stochastic Galerkin discretization are computed on the time-continuous level. Then, we solve the resulting semi-discrete forward and backward
schemes with the Runge-Kutta method. To illustrate the feasibility of the approach,
we apply the method to a stochastic advection and a stochastic equation of Burgers&#39; type. The results show that the method is able to identify the distribution parameters
of the random variable in the uncertain differential equation even if discontinuities are
present.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2019-0221},
url = {https://global-sci.com/article/79732/parameter-identification-in-uncertain-scalar-conservation-laws-discretized-with-the-discontinuous-stochastic-galerkin-scheme}
}