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Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation. (English) Zbl 1087.65004
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.
MSC:
65C30Stochastic differential and integral equations
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
60H15Stochastic partial differential equations
35R60PDEs with randomness, stochastic PDE
35J25Second order elliptic equations, boundary value problems
65C05Monte Carlo methods