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Zbl 1075.65006
Deb, Manas K.; Babuška, Ivo M.; Oden, J. Tinsley
Solution of stochastic partial differential equations using Galerkin finite element techniques. (English)
[J] Comput. Methods Appl. Mech. Eng. 190, No. 48, 6359-6372 (2001). ISSN 0045-7825

Summary: 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.

MSC 2000:: *65C30 Stochastic differential and integral equations
65N30 Finite numerical methods (BVP of PDE)

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