This talk is devoted to the Galerkin projection of highly nonlinear random quantities.
The dependency on a random input is described by Haar-type wavelet systems.
The classical Haar sequence has been used by Pettersson, Iaccarino, Nordström (2014) for a hyperbolic stochastic Galerkin formulation of the one-dimensional Euler equations.
We generalize their approach to several multi-dimensional systems with Lipschitz continuous and non-polynomial flux functions.
Theoretical results are illustrated numerically by a genuinely multidimensional CWENO reconstruction that allows for higher-order discretizations of balance laws.