A posteriori error estimation for stochastic static problems

Archive ouverte : Article de revue

Mac, Hung | Clenet, Stéphane

Edité par HAL CCSD ; Institute of Electrical and Electronics Engineers

International audience. To solve stochastic static field problems, a discretization by the Finite Element Method can be used. A system of equations is obtained with the unknowns (scalar potential at nodes for example) being random variables. To solve this stochastic system, the random variables can be approximated in a finite dimension functional space - a truncated polynomial chaos expansion. The error between the exact solution and the approximated one depends not only on the spatial mesh but also on the discretization along the stochastic dimension. In this paper, we propose an a posteriori estimation of the error due to the discretization along the stochastic dimension.

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