A posteriori error estimator for harmonic A‐φ formulation

Zuqi Tang ^[1] ; Yvonnick Le Menach ^[1] ; Emmanuel Creuse ^[1] ; Serge Nicaise ^[2] ; Francis Piriou ^[1] ; Nicolas Nemitz ^[3]
1. [1] Lille 1 University
  
  Lille 1 University
  
  Arrondissement de Lille, Francia
2. [2] Université de Valenciennes et du Haut Cambrésis
3. [3] THEMIS
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Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 32, Nº 4 (Special Issue: Modelling of magnetic and electric circuits), 2013, págs. 1219-1229
Idioma: inglés
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Resumen
- 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‐φ 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‐φ 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.