  Most approximation methods in high dimensions exploit smoothness of the
function being approximated. These methods provide poor convergence results for
non-smooth 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.
