Uncertain parameters in mathematical models are often described by means of random numbers, random fields or random processes. This approach is particularly effective if the stochastic characteristics of the uncertain parameters is accurately known. When that is not the case, however, an uncertainty representation using alternative models, such as intervals or fuzzy numbers, may be more appropriate.
In this talk we consider partial differential equations with interval and fuzzy parameters. The uncertain equation is reformulated as a parametric PDE and solved by means of polynomial chaos technique. An algebraic multigrid method is used to solve the coupled PDE system that is obtained by applying a Galerkin projection in the parameter space. We analyse the convergence of the multigrid method and illustrate its performance by means of some numerical experiments. A comparison is made with the Kriging method, a popular alternative for solving PDEs with interval and fuzzy uncertainties.