Space-time residual-based a posteriori estimators for the A/Phi magneto dynamic formulation of the Maxwell system

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

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

In this paper, an a posteriori residual error estimator is proposed for the A/Phi magnetodynamic Maxwell system given in its potential and space/time formulation and solved by a Finite Element method. The reliability as well as the e ciency of the estimator are established for several norms. Then, numerical tests are performed, allowing to illustrate the obtained theoretical results.

Mots clés: Maxwell equations; Potential formulation; Space-time a posteriori estimators; Finite element method.

Mots clés: Finite element method

Domaines: Analyse numérique [math.NA]

Emmanuel Creusé, Serge Nicaise, Roberta Tittarelli. Space-time residual-based a posteriori estimators for the A/Phi magneto dynamic formulation of the Maxwell system. Computational Methods in Applied Mathematics, 2014, 14 (4), pp.429-460. ⟨10.1515/cmam-2014-0015⟩. ⟨hal-00921116⟩