A survey in mathematics for industry: Polynomial chaos for the approximation of uncertainties: Chances and limits

In technical applications, uncertainties are a topic of increasing interest. During the last years the Polynomial Chaos of Wiener (Amer. J. Math. 60(4), 897936, 1938) was revealed to be a cheap alternative to Monte Carlo simulations. In this paper we apply Polynomial Chaos to stationary and transient problems, both from academics and from industry. For each of the applications, chances and limits of Polynomial Chaos are discussed. The presented problems show the need for new theoretical results.