A negative-norm least-squares method for time-harmonic Maxwell equations

Dylan M. Copeland

doi:10.1016/j.jmaa.2011.09.004

A negative-norm least-squares method for time-harmonic Maxwell equations

Dylan M. Copeland

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

3 Scopus citations

Abstract

This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.

Original language	English (US)
Pages (from-to)	303-317
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	388
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2011.09.004
State	Published - Apr 2012
Externally published	Yes

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10.1016/j.jmaa.2011.09.004

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title = "A negative-norm least-squares method for time-harmonic Maxwell equations",

abstract = "This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. {\textcopyright} 2011 Elsevier Inc.",

author = "Copeland, {Dylan M.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The author thanks Prof. Joseph E. Pasciak for helpful discussions in developing the theory for this work. This publication is based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2012",

month = apr,

doi = "10.1016/j.jmaa.2011.09.004",

language = "English (US)",

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journal = "Journal of Mathematical Analysis and Applications",

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AU - Copeland, Dylan M.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The author thanks Prof. Joseph E. Pasciak for helpful discussions in developing the theory for this work. This publication is based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2012/4

Y1 - 2012/4

N2 - This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.

AB - This paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.

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U2 - 10.1016/j.jmaa.2011.09.004

DO - 10.1016/j.jmaa.2011.09.004

M3 - Article

SN - 0022-247X

VL - 388

SP - 303

EP - 317

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

A negative-norm least-squares method for time-harmonic Maxwell equations

Abstract

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