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Residual-based a posteriori error estimation for a stochastic magnetostatic problem

Duc Hung Mac 1 Zuqi Tang 1 Stephane Clenet 1 Emmanuel Creusé 2, 3
1 L2EP - Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697
2 RAPSODI - Reliable numerical approximations of dissipative systems
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
3 LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : In this paper, we propose an a posteriori error estimator for the numerical approximation of a stochastic magnetostatic problem, whose solution depends on the spatial variable but also on a stochastic one. The spatial discretization is performed with finite elements and the stochastic one with a polynomial chaos expansion. As a consequence, the numerical error results from these two levels of discretization. In this paper, we propose an error estimator that takes into account these two sources of error, and which is evaluated from the residuals.
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https://hal.archives-ouvertes.fr/hal-01243687
Contributor : Emmanuel Creusé Connect in order to contact the contributor
Submitted on : Tuesday, December 15, 2015 - 11:56:47 AM
Last modification on : Wednesday, March 23, 2022 - 3:51:21 PM

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CNRS | INSMI | INRIA | TDS-MACS | UNIV-LILLE | UNIV-HESAM | ARTS-ET-METIERS-SCIENCES-ET-TECHNOLOGIES | L2EP | ANR | INRIA2

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Duc Hung Mac, Zuqi Tang, Stephane Clenet, Emmanuel Creusé. Residual-based a posteriori error estimation for a stochastic magnetostatic problem. Journal of Computational and Applied Mathematics, Elsevier, 2015, 289, pp.51-67. ⟨10.1016/j.cam.2015.03.027⟩. ⟨hal-01243687⟩

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