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In this paper, we consider Burgers' equation with uncertain boundary andinitial conditions. The polynomial chaos (PC) approach yields a hyperbolicsystem of deterministic equations, which can be solved by several numericalmethods. Here, we apply the correction procedure via reconstruction (CPR) usingsummation-by-parts operators. We focus especially on stability, which is provenfor CPR methods and the systems arising from the PC approach. Due to the usageof split-forms, the major challenge is to construct entropy stable numericalfluxes. For the first time, such numerical fluxes are constructed for allsystems resulting from the PC approach for Burgers' equation. In numericaltests, we verify our results and show also the advantage of the given ansatzusing CPR methods. Moreover, one of the simulations, i.e. Burgers' equationequipped with an initial shock, demonstrates quite fascinating observations.The behaviour of the numerical solutions from several methods (finite volume,finite difference, CPR) differ significantly from each other. Through carefulinvestigations, we conclude that the reason for this is the high sensitivity ofthe system to varying dissipation. Furthermore, it should be stressed that thesystem is not strictly hyperbolic with genuinely nonlinear or linearlydegenerate fields.

Stability of Correction Procedure via Reconstruction With Summation-by-Parts Operators for Burgers' Equation Using a Polynomial Chaos Approach