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Numerical Mathematics and Advanced Applications 2009
Burgers' equation with uncertain initial and boundary conditions is approximated using a polynomial chaos expansion approach where the solution is represented as a series of stochastic, orthogonal polynomials. Even though the analytical solution is smooth, a number of discontinuities emerge in the truncated system. The solution is highly sensitive to the propagation speed of these discontinuities. High-resolution schemes are needed to accurately capture the behavior of the solution. Thedoi:10.1007/978-3-642-11795-4_79 fatcat:qinfetijqjcjtd2pu6wp2y7ufm