A posteriori error estimator for harmonic A‐φ formulation

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

Purpose - In this paper, the aim is to propose a residual-based error estimator to evaluate the numerical error induced by the computation of the electromagnetic systems using a finite element method in the case of the harmonic A-? formulation. Design/methodology/approach - The residual based error estimator used in this paper verifies the mathematical property of global and local error estimation (reliability and efficiency). Findings - This estimator used is based on the evaluation of quantities weakly verified in the case of harmonic A-? formulation. Originality/value - In this paper, it is shown that the proposed estimator, based on the mathematical developments, is hardness in the case of the typical applications.

Mots clés: A posteriori error estimation; Eddy current problems; Error analysis; Finite element analysis; Finite element method; Harmonic formulation; Slinky

Domaines: Analyse numérique [math.NA]

Zuqi Tang, Yvonnick Le Menach, Emmanuel Creusé, Serge Nicaise, Francis Piriou, et al.. A posteriori error estimator for harmonic A‐φ formulation. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2013, 32 (4), pp.1219-1229. ⟨10.1108/03321641311317040⟩. ⟨hal-00910309⟩