Abstract
Intrusive Uncertainty Quantification methods such as stochastic Galerkin
are gaining popularity, whereas the classical stochastic Galerkin
approach is not ensured to preserve hyperbolicity of the underlying
hyperbolic system. We present a modification of this method that
uses a slope limiter to retain admissible solutions of the system,
while providing high-order approximations in the physical and stochastic
space. This is done using spatial discontinuous Galerkin and a Multi-Element
stochastic Galerkin ansatz in the random space. We analyze the convergence
of the resulting scheme and apply it to the compressible Euler equations
with different uncertain initial states. The numerical results underline
the strength of our method if discontinuities are present in the
uncertainty of the solution.
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