Finite elements for stochastic media problems

We consider discretization methods for stochastic partial differential equations, which are used to model media with stochastic properties. The Wick product formulation of the stochastic PDE is used, and it is shown how it may be discretized both spatially and in the stochastic part. A stochastic Variational principle serves as the guideline for the discretization procedure. It is shown that both the projection onto the Wiener chaos and the Hermite-transform lead to the same fully discrete equations. The application examples show that there are other advantageous bases besides the Karhunen-Loeve expansion, and that the methods may be used in a variety of settings. (C) 1999 Elsevier Science S.A. All rights reserved.