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Zbl 1087.65004
Babuška, Ivo; Tempone, Raúl; Zouraris, Georgios E.
Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation. (English)
[J] Comput. Methods Appl. Mech. Eng. 194, No. 12-16, 1251-1294 (2005). ISSN 0045-7825

The authors study a linear elliptic problem with uncertainty. The main objective of this paper is the probabilistic treatment of uncertainly addressing the problem of solving linear elliptic boundary value problems with stochastic coefficients. A number of theorems and estimates are developed for theoretical foundation and finally these are experimented for illustration.
[Prabhat Kumar Mahanti (Saint John)]

MSC 2000:: *65C30 Stochastic differential and integral equations
65N30 Finite numerical methods (BVP of PDE)
65N15 Error bounds (BVP of PDE)
60H15 Stochastic partial differential equations
35R60 PDE with randomness
35J25 Second order elliptic equations, boundary value problems
65C05 Monte Carlo methods

Keywords: perturbation estimates; error estimates; adaptive methods; error control; finite elements; numerical examples; stochastic elliptic equation; Karhunen-Loève expansion; Monte Carlo method

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