A guaranteed equilibrated error estimator for the $\mathbf{A}-\varphi$ and $\mathbf{T}-\Omega$ magnetodynamic harmonic formulations of the Maxwell system

Emmanuel Creusé (1, 2) , Serge Nicaise (3) , Roberta Tittarelli (4, 5, 2)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
4 EDF R&D - EDF R&D
5 L2EP - Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697

In this paper, a guaranteed equilibrated error estimator is proposed for the harmonic magnetodynamic formulation of the Maxwell's system. This system is recast in two classical potential formulations, which are solved by a Finite Element method. The equilibrated estimator is built starting from these dual problems and is consequently available to estimate the error of both numerical resolutions. The estimator reliability and efficiency without generic constants are established. Then, numerical tests are performed, allowing to illustrate the obtained theoretical results.

Mots clés: finite element method AMS (MOS) subject classification 35Q61; potential formulation; a posteriori estimators; 65N15; 65N50; 65N30; Maxwell equations

Domaines: Analyse numérique [math.NA]; Mathématiques [math]

Emmanuel Creusé, Serge Nicaise, Roberta Tittarelli. A guaranteed equilibrated error estimator for the $\mathbf{A}-\varphi$ and $\mathbf{T}-\Omega$ magnetodynamic harmonic formulations of the Maxwell system. IMA Journal of Numerical Analysis, 2017, 37 (2), pp.750-773. ⟨10.1093/imanum/drw026⟩. ⟨hal-01110258⟩