TY - JOUR
T1 - A survey in mathematics for industry
T2 - Polynomial chaos for the approximation of uncertainties: Chances and limits
AU - Augustin, F.
AU - Gilg, A.
AU - Paffrath, M.
AU - Rentrop, P.
AU - Wever, U.
PY - 2008/4
Y1 - 2008/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=41149132850&partnerID=8YFLogxK
U2 - 10.1017/S0956792508007328
DO - 10.1017/S0956792508007328
M3 - Review article
AN - SCOPUS:41149132850
SN - 0956-7925
VL - 19
SP - 149
EP - 190
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
IS - 2
ER -