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Numerische Mathematik

, Volume 73, Issue 3, pp 329–372 | Cite as

A hierarchy of approximate models for the Maxwell equations

  • Pierre-Arnaud Raviart
  • Eric Sonnendrücker

Summary.

In this paper we perform an asymptotic study of the Maxwell equations with respect to the small parameter \(\eps=v/c\) where \(v\) is the characteristic velocity associated with the physical problem and \(c\) is the speed of light. This enables us to derive the quasistatic and Darwin models as respectively first and second order approximations of the Maxwell equations. Moreover, an interpretation of the obtained variational formulations gives us the appropriate boundary conditions for these models.

Mathematics Subject Classification (1991):35J50, 35J55, 41A60, 78A25, 78A30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Pierre-Arnaud Raviart
    • 1
  • Eric Sonnendrücker
    • 2
  1. 1.CMAP Ecole Polytechnique, F-91128 Palaiseau Cedex, France FR
  2. 2.CEA Centre d'Etudes de Limeil-Valenton, F-94195 Villeneuve-St-Georges Cedex, France; e-mail: sonnendr@limeil.cea.fr FR

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