A posteriori error estimation for stochastic static problems

Hung Mac (1) , Stéphane Clenet (1)

1 L2EP - Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697

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.

Mots clés: Stochastic Problems; Finte Element Method; Polynomial Chaos Expansion; Static Fields; Error estimation

Domaines: Electromagnétisme

Hung Mac, Stéphane Clenet. A posteriori error estimation for stochastic static problems. IEEE Transactions on Magnetics, 2014, 50 (2), ⟨10.1109/TMAG.2013.2281103⟩. ⟨hal-01017925⟩