Quantifying Uncertainty
Deb, M.K., Babuska, I.M., and Oden, J.T. "Solution of stochastic partial differential equations using Galerkin finite element techniques" Comput. Methods Appl. Mech. Engrg..
vol. 190.
2001.
pp. 6359--6372.
This paper presents a framework for the construction of Galerkin approximations of elliptic boundary-value problems with stochastic input data. A variational formulation is developed which allows, among others, numerical treatment by the finite element method; a theory of a posteriori error estimation and corresponding adaptive approaches based on practical experience can be utilized. The paper develops a foundation for treating stochastic partial differential equations (PDEs) which can be further developed in many directions