  The subject of this work is an adaptive stochastic Galerkin finite element
method for parametric or random elliptic partial differential equations, which
generates sparse product polynomial expansions with respect to the parametric
variables of solutions. For the corresponding spatial approximations, an
independently refined finite element mesh is used for each polynomial
coefficient. The method relies on multilevel expansions of input random fields
and achieves error reduction with uniform rate. In particular, the saturation
property for the refinement process is ensured by the algorithm. The results
are illustrated by numerical experiments, including cases with random fields of
low regularity.
