In recent years it has become more and more important to model and simulate boundary value problems with random input parameters. If a statistical description of the input data is available, one can mathematically describe data and solutions as random fields and aim at the computation of corresponding deterministic statistics of the unknown random solution. Applications are, besides traditional engineering, for example biomedical or biomechanical processes. To simulate biomechanical processes one has, on the one hand, uncertain domains arising from e.g. tomographic data. On the other hand, one often has only estimates on the material parameters.

Uncertainty might stem from the loading, the coefficients of the differential operator, or the domain of definition. In case of random loadings, the random solution depends linearly on the random input data. But this is not valid any more if the differential operator’s coefficients or the domain of definition are random. Consequently, innovative methods must be developed in order to overcome the curse of dimension which is induced by the random process.