A posteriori residual error estimators with mixed boundary conditions for quasi-static electromagnetic problems

Zuqi Tang (1) , Y. Le Menach (2) , Emmanuel Creusé (3, 4) , Serge Nicaise (5) , Francis Piriou (2) , Nicolas Nemitz (6)

1 SERENA - Simulation for the Environment : Reliable and Efficient Numerical Algorithms
2 L2EP - Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697
3 RAPSODI - Reliable numerical approximations of dissipative systems
4 LPP - Laboratoire Paul Painlevé - UMR 8524
5 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
6 EDF R&D - EDF R&D

The purpose of this paper is to propose some a posteriori residual error estimators (REEs)to evaluate the accuracy of the finite element method for quasi-static electromagnetic problems with mixed boundary conditions. Both classical magnetodynamic A-ϕ and T-Ω formulations in harmonic case are analysed. As an example of application the estimated error maps of an electromagnetic system are studied. At last, a remeshing process is done according to the estimated error maps.

Domaines: Analyse numérique [math.NA]

Zuqi Tang, Y. Le Menach, Emmanuel Creusé, Serge Nicaise, Francis Piriou, et al.. A posteriori residual error estimators with mixed boundary conditions for quasi-static electromagnetic problems. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2015, 34 (3), pp.724-739. ⟨10.1108/COMPEL-10-2014-0256⟩. ⟨hal-01243637⟩