Finite elements for stochastic media problems

We consider discretization methods for stochastic partial differential equa tions, which are used to model media with stochastic properties. The Wick p roduct formulation of the stochastic PDE is used, and it is shown how it ma y be discretized both spatially and in the stochastic part. A stochastic Va riational principle serves as the guideline for the discretization procedur e. It is shown that both the projection onto the Wiener chaos and the Hermi te-transform lead to the same fully discrete equations. The application exa mples show that there are other advantageous bases besides the Karhunen-Loe ve expansion, and that the methods may be used in a variety of settings. (C ) 1999 Elsevier Science S.A. All rights reserved.