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Edge finite elements for the approximation of Maxwell resolventoperator

Published online by Cambridge University Press:  15 May 2002

Daniele Boffi  and
Lucia Gastaldi
Daniele Boffi
Affiliation:
Dipartimento di Matematica, Università di Pavia, 27100 Pavia, Italy. [email protected].
Lucia Gastaldi
Affiliation:
Dipartimento di Matematica, Università di Brescia, 25133 Brescia, Italy. [email protected].
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Abstract

In this paper we consider the Maxwell resolvent operator and its finite elementapproximation. In this framework it is natural the use of the edge elementspaces and to impose the divergence constraint in a weaksense with the introduction of a Lagrange multiplier, followingan idea by Kikuchi [14].We shall review some of the known properties for edge elementapproximations and prove some new result. In particular we shall prove auniform convergence in the L 2 norm for the sequence of discrete operators.These results, together with a general theory introduced by Brezzi, Rappaz andRaviart [8], allow an immediate proof of convergence for thefinite element approximation of the time-harmonicMaxwell system.

Keywords

Edge finite elementstime-harmonic Maxwell's equationsmixed finite elements.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 2 , March 2002 , pp. 293 - 305
Copyright
© EDP Sciences, SMAI, 2002

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