Analyses of exact problems: Second-order models

Franck Assous, Patrick Ciarlet, Simon Labrunie

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This chapter is devoted to an alternative, second-order formulation of the Maxwell’s equations. We rigorously justify the process we outlined in Sect. 1.5.3. This new formulation is especially relevant for computational applications, as it admits several variational formulations, which can be simulated by versatile finite element methods. Our attention will be focused on three issues: equivalence of the second-order equations with the original, first-order equations studied in Chap. 5, the well-posedness of the new formulation and the regularity of its solution, as we did in that chapter. We also study how to take into account the conditions on the divergence of the fields, incorporating them explicitly at some point in the variational formulations. To these ends, we shall again rely on the mathematical tools introduced in Chaps. 2, 3 and 4, as well as on the specific properties of the spaces of electromagnetic fields introduced in Chap. 6.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
Number of pages46
StatePublished - 2018
Externally publishedYes

Publication series

NameApplied Mathematical Sciences (Switzerland)
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.


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