Abstract:
Real-life engineering problems are often subject to significant parameter uncertainties. Including such uncertainties in the underlying mathematical model results in a multiparametric problem, in which the stochastic dimension of the system is approximated by a finite, but possibly large, number of parameters. Sparse stochastic collocation algorithms may then be used to resolve the dependence of the solution on the input parameters. Optimal rates of convergence are observed when the solution depends analytically on the input parameters. In the case of eigenvalue problems special care must be taken in order to make solutions corresponding to different parameter values comparable.