RT Journal Article ID 08cb2f2c0b0f0085 A1 Fuchs, Barbara A1 Garcke, Jochen T1 SIMPLEX STOCHASTIC COLLOCATION FOR PIECEWISE SMOOTH FUNCTIONS WITH KINKS JF International Journal for Uncertainty Quantification JO IJUQ YR 2020 FD 2020-02-06 VO 10 IS 1 SP 1 OP 24 K1 uncertainty quantification K1 stochastic collocation K1 energy and the environment K1 stochastic discontinuity K1 adaptivity K1 Delaunay triangulation K1 gas networks AB Most approximation methods in high dimensions exploit smoothness of the function being approximated. These methods provide poor convergence results for nonsmooth functions with kinks. For example, such kinks can arise in the uncertainty quantification of quantities of interest for gas networks. This is due to the regulation of the gas flow, pressure, or temperature. But, one can exploit that, for each sample in the parameter space it is known if a regulator was active or not, which can be obtained from the result of the corresponding numerical solution. This information can be exploited in a stochastic collocation method. We approximate the function separately on each smooth region by polynomial interpolation and obtain an approximation to the kink. Note that we do not need information about the exact location of kinks, but only an indicator assigning each sample point to its smooth region. We obtain a global order of convergence of (p + 1)/d, where p is the degree of the employed polynomials and d the dimension of the parameter space. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,64e608bf6c8f0cc8,08cb2f2c0b0f0085.html