Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

Andrea Bonito; Jean-Luc Guermond

doi:10.1090/S0025-5718-2011-02464-6

Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

Andrea Bonito, Jean-Luc Guermond

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H-α with α ∈ (1/2, 1). The method is shown to be convergent and spectrally correct. © 2011 American Mathematical Society.

Original language	English (US)
Pages (from-to)	1887-1887
Number of pages	1
Journal	Mathematics of Computation
Volume	80
Issue number	276
DOIs	https://doi.org/10.1090/S0025-5718-2011-02464-6
State	Published - 2011
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The first author was partially supported by the NSF grant DMS-0914977.The second author was partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).The third author was partially supported by the NSF grant DMS-07138229.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Access to Document

10.1090/S0025-5718-2011-02464-6

Cite this

@article{13b60593c28340eb9536d50760b334c7,

title = "Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements",

abstract = "We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H-α with α ∈ (1/2, 1). The method is shown to be convergent and spectrally correct. {\textcopyright} 2011 American Mathematical Society.",

author = "Andrea Bonito and Jean-Luc Guermond",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The first author was partially supported by the NSF grant DMS-0914977.The second author was partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).The third author was partially supported by the NSF grant DMS-07138229. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2011",

doi = "10.1090/S0025-5718-2011-02464-6",

language = "English (US)",

volume = "80",

pages = "1887--1887",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

number = "276",

}

TY - JOUR

T1 - Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

AU - Bonito, Andrea

AU - Guermond, Jean-Luc

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The first author was partially supported by the NSF grant DMS-0914977.The second author was partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).The third author was partially supported by the NSF grant DMS-07138229. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2011

Y1 - 2011

N2 - We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H-α with α ∈ (1/2, 1). The method is shown to be convergent and spectrally correct. © 2011 American Mathematical Society.

AB - We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H-α with α ∈ (1/2, 1). The method is shown to be convergent and spectrally correct. © 2011 American Mathematical Society.

UR - http://hdl.handle.net/10754/597604

UR - http://www.ams.org/jourcgi/jour-getitem?pii=S0025-5718-2011-02464-6

UR - http://www.scopus.com/inward/record.url?scp=79957551938&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-2011-02464-6

DO - 10.1090/S0025-5718-2011-02464-6

M3 - Article

SN - 0025-5718

VL - 80

SP - 1887

EP - 1887

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 276

ER -

Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this