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Two Guaranteed Equilibrated Error Estimators for Harmonic Formulations in Eddy Current Problems

Archive ouverte : Article de revue

Creusé, Emmanuel | Le Menach, Yvonnick | Nicaise, Serge | Piriou, Francis | Tittarelli, Roberta

Edité par HAL CCSD ; Elsevier

International audience. In this paper, two guaranteed equilibrated error estimators are proposed and compared for the 3D harmonic magnetodynamic problem of Maxwell's system. This system is recasted in the classical A − ϕ potential formulation or, equivalently , in the T − Ω potential formulation, and it is solved by the Finite Element method. The first equilibrated estimator presented is built starting from these two complementary problems, the other one is built starting from the A − ϕ numerical solution uniquely by a flux reconstruction technique. The equivalence between errors and estimators is established. Afterwards, an analytical benchmark test illustrates the obtained theoretical results and a physical benchmark test shows the efficiency of these two estimators.

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