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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 14, Issue 4


Space-Time Residual-Based A Posteriori Estimators for the A−ϕ Magnetodynamic Formulation of the Maxwell System

Emmanuel Creusé
  • Laboratoire Paul Painlevé UMR 8524 and EPI SIMPAF INRIA Lille Nord Europe, Université Lille 1, Cité Scientifique, 59655 Villeneuve d'Ascq Cedex, France
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/ Serge Nicaise
  • Laboratoire de Mathématiques et leurs Applications de Valenciennes FR CNRS 2956, Université de Valenciennes et du Hainaut Cambrésis, Institut des Sciences et Techniques de Valenciennes, 59313 Valenciennes Cedex 9, France
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/ Roberta Tittarelli
  • Laboratoire Paul Painlevé UMR 8524, Laboratoire d' Electrotechnique et d' Electronique de Puissance de Lille, Université Lille 1, Cité Scientifique, 59655 Villeneuve d'Ascq Cedex; and EDF Division Recherche et Développement, 1, avenue du Général de Gaulle, 92141 Clamart Cedex, France
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Published Online: 2014-05-23 | DOI: https://doi.org/10.1515/cmam-2014-0015


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

Keywords: Maxwell Equations; Potential Formulation; Space-Time A Posteriori Estimators; Finite Element Method

MSC: 35Q61; 65N30; 65N15; 65N50

About the article

Received: 2013-12-19

Revised: 2014-04-24

Accepted: 2014-05-02

Published Online: 2014-05-23

Published in Print: 2014-10-01

Funding Source: EDF R&D

Funding Source: Labex CEMPI

Award identifier / Grant number: ANR-11-LABX-0007-01

Funding Source: MEDEE project

Funding Source: European Regional Development Fund

Funding Source: Region Nord-Pas-de-Calais

Citation Information: Computational Methods in Applied Mathematics, Volume 14, Issue 4, Pages 429–460, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2014-0015.

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