Edge finite elements for the approximation of Maxwell resolvent operator
Dipartimento di Matematica, Università di Pavia, 27100 Pavia, Italy. email@example.com.
2 Dipartimento di Matematica, Università di Brescia, 25133 Brescia, Italy. firstname.lastname@example.org.
Revised: 23 January 2002
In this paper we consider the Maxwell resolvent operator and its finite element approximation. In this framework it is natural the use of the edge element spaces and to impose the divergence constraint in a weak sense with the introduction of a Lagrange multiplier, following an idea by Kikuchi . We shall review some of the known properties for edge element approximations and prove some new result. In particular we shall prove a uniform convergence in the L2 norm for the sequence of discrete operators. These results, together with a general theory introduced by Brezzi, Rappaz and Raviart , allow an immediate proof of convergence for the finite element approximation of the time-harmonic Maxwell system.
Mathematics Subject Classification: 65N25 / 65N30
Key words: Edge finite elements / time-harmonic Maxwell's equations / mixed finite elements.
© EDP Sciences, SMAI, 2002