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

Emmanuel Creusé (1, 2) , Yvonnick Le Menach (3) , Serge Nicaise (4) , Francis Piriou (3) , Roberta Tittarelli (5, 1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 RAPSODI - Reliable numerical approximations of dissipative systems
3 L2EP - Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697
4 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
5 ENSMM - Ecole Nationale Supérieure de Mécanique et des Microtechniques

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.

Mots clés: Nédélec and Raviart-Thomas elements; Finite Element Method; eddy current problem; time-harmonic analysis; 3D; A posteriori estimator

Domaines: Analyse numérique [math.NA]

Emmanuel Creusé, Yvonnick Le Menach, Serge Nicaise, Francis Piriou, Roberta Tittarelli. Two Guaranteed Equilibrated Error Estimators for Harmonic Formulations in Eddy Current Problems. Computers & Mathematics with Applications, 2019, 77 (6), pp.1549-1562. ⟨10.1016/j.camwa.2018.08.046⟩. ⟨hal-01955692⟩