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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)
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References:
[1] Ainsworth, M.; Oden, J. T.: A posteriori error estimation in finite element analysis. (2000) · Zbl 1008.65076
[2] Amanov, T. I.: Spaces of differentiable functions with dominant mixed derivatives. (1976)
[3] I. Babuška, On Randomized Solution of Laplace’s Equation, Casopis Pest Mat., 1961
[4] Babuška, I.; Strouboulis, T.: The finite element method and its reliability. (2001) · Zbl 0995.65501
[5] M. Deb, I. Babuška, J.T. Oden, Stochastic Finite Element using Galerkin Approximation, Fifth US National Congress on Computational Mechanics, Boulder, 1999
[6] M. Deb, Solution of stochastic partial differential equations (SPDEs) using Galerkin method: theory and applications, Ph.D. Dissertation, The University of Texas, Austin, 2000
[7] Elishakoff, I.; Ren, Y.: The bird’s eye view on finite element method for structures with large stochastic variations. Comput. methods appl. Mech. engrg. 168, No. 1--4, 51-61 (1999) · Zbl 0953.74063
[8] Ghanem, R.; Spanos, P.: Stochastic finite elements: A spectral approach. (1991) · Zbl 0722.73080
[9] Ghanem, R.: Ingredients for a general purpose stochastic finite elements implementation. Comput. methods appl. Mech. engrg. 168, No. 1--4, 19-33 (1999) · Zbl 0943.65008
[10] Holden, H.; Oksendal, B.; Uboe, J.; Zhang, T. S.: Stochastic partial differential equations -- A modeling white noise functional approach. (1966)
[11] Kleiber, M.; Hien, T. D.: The stochastic finite element method. (1992) · Zbl 0902.73004
[12] Loeve, M.: Probability theory. (1977) · Zbl 0359.60001
[13] Oksendal, B.: Stochastic differential equations -- an introduction with application. (1998)
[14] G.I. Schueller and H.J. Pradwarter, Computational stochastic mechanics -- current developments and prospects, in: S. Idelsohn, E. Onate, E. Dvorkin (Eds.), Computational Mechanics: New Trends and Applications, CIMNE, Barcelona, 1998