Residual and Equilibrated Error Estimators for Magnetostatic Problems Solved by Finite Element Method

Zuqi Tang (1) , Yvonnick Le Menach (1) , Emmanuel Creusé (2, 3) , Serge Nicaise (4) , Francis Piriou (1) , Nicolas Nemitz (5)

1 L2EP - Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 SIMPAF - SImulations and Modeling for PArticles and Fluids
4 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
5 EDF R&D - EDF R&D

In finite element computations, the choice of the mesh is crucial to obtain accurate solutions. In order to evaluate the quality of the mesh, a posteriori error estimators can be used. In this paper, we develop residual-based error estimators for magnetostatic problems with both classical formulations in term of potentials used, as well as the equilibrated error estimator. We compare their behaviors on some numerical applications, to understand the interest of each of them in the remeshing process.

Domaines: Analyse numérique [math.NA]

Zuqi Tang, Yvonnick Le Menach, Emmanuel Creusé, Serge Nicaise, Francis Piriou, et al.. Residual and Equilibrated Error Estimators for Magnetostatic Problems Solved by Finite Element Method. IEEE Transactions on Magnetics, 2013, 49 (12), pp.5715-5723. ⟨10.1109/TMAG.2013.2271993⟩. ⟨hal-00910314⟩