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Using standard intrusive techniques when solving hyperbolic conservation laws with uncertainties can lead to oscillatory solutions as well as nonhyperbolic moment systems. The Intrusive Polynomial Moment (IPM) method ensures hyperbolicity of the moment system while restricting oscillatory over-and undershoots to specified bounds. In this contribution, we derive a second-order discretization of the IPM moment system which fulfills the maximum principle. This task is carried out by investigatingdoi:10.5802/smai-jcm.42 fatcat:en7unti23janhaq3bujcjehbqa