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A posteriori error estimation for stochastic static problems

Article dans une revue avec comité de lecture
Author
MAC, Hung
13338 Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697 [L2EP]
CLENET, Stéphane
13338 Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697 [L2EP]

URI
http://hdl.handle.net/10985/8319
DOI
10.1109/TMAG.2013.2281103
Date
2014
Journal
IEEE Transactions on Magnetics

Abstract

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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