TY - CHAP

T1 - Analyses of exact problems

T2 - Second-order models

AU - Assous, Franck

AU - Ciarlet, Patrick

AU - Labrunie, Simon

N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85067949848&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-70842-3_7

DO - 10.1007/978-3-319-70842-3_7

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AN - SCOPUS:85067949848

T3 - Applied Mathematical Sciences (Switzerland)

SP - 267

EP - 312

BT - Applied Mathematical Sciences (Switzerland)

ER -