Solution of stochastic partial differential equations using Galerkin finite element techniques

This paper presents a framework for the construction of Galerkin approximat ions of elliptic boundary-value problems with stochastic input data. A vari ational formulation is developed which allows, among others, numerical trea tment by the finite element method; a theory of a posteriori error estimati on and corresponding adaptive approaches based on practical experience can be utilized. The paper develops a foundation for treating stochastic partia l differential equations (PDEs) which can be further developed in many dire ctions. (C) 2001 Published by Elsevier Science B.V.