# Edge finite elements for the approximation of Maxwell resolvent operator

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 36, Issue: 2, page 293-305
- ISSN: 0764-583X

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topBoffi, Daniele, and Gastaldi, Lucia. "Edge finite elements for the approximation of Maxwell resolvent operator." ESAIM: Mathematical Modelling and Numerical Analysis 36.2 (2010): 293-305. <http://eudml.org/doc/194105>.

@article{Boffi2010,

abstract = {
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 [14].
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 [8], allow an immediate proof of convergence for the
finite element approximation of the time-harmonic
Maxwell system.
},

author = {Boffi, Daniele, Gastaldi, Lucia},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Edge finite elements; time-harmonic Maxwell's equations; mixed finite elements.; edge finite elements; time-harmonic Maxwell's equations, mixed finite elements; convergence},

language = {eng},

month = {3},

number = {2},

pages = {293-305},

publisher = {EDP Sciences},

title = {Edge finite elements for the approximation of Maxwell resolvent operator},

url = {http://eudml.org/doc/194105},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Boffi, Daniele

AU - Gastaldi, Lucia

TI - Edge finite elements for the approximation of Maxwell resolvent operator

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 2

SP - 293

EP - 305

AB -
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 [14].
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 [8], allow an immediate proof of convergence for the
finite element approximation of the time-harmonic
Maxwell system.

LA - eng

KW - Edge finite elements; time-harmonic Maxwell's equations; mixed finite elements.; edge finite elements; time-harmonic Maxwell's equations, mixed finite elements; convergence

UR - http://eudml.org/doc/194105

ER -

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## Citations in EuDML Documents

top- Paul Houston, Ilaria Perugia, Anna Schneebeli, Dominik Schötzau, Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case
- Paul Houston, Ilaria Perugia, Anna Schneebeli, Dominik Schötzau, Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case

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