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Solution of stochastic partial differential equations using Galerkin finite element techniques. (English) Zbl 1075.65006
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:
65C30Stochastic differential and integral equations
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)