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

Handle URI:
http://hdl.handle.net/10754/597332
Title:
A negative-norm least-squares method for time-harmonic Maxwell equations
Authors:
Copeland, Dylan M.
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.
Citation:
Copeland DM (2012) A negative-norm least-squares method for time-harmonic Maxwell equations. Journal of Mathematical Analysis and Applications 388: 303–317. Available: http://dx.doi.org/10.1016/j.jmaa.2011.09.004.
Publisher:
Elsevier BV
Journal:
Journal of Mathematical Analysis and Applications
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Apr-2012
DOI:
10.1016/j.jmaa.2011.09.004
Type:
Article
ISSN:
0022-247X
Sponsors:
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).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorCopeland, Dylan M.en
dc.date.accessioned2016-02-25T12:30:53Zen
dc.date.available2016-02-25T12:30:53Zen
dc.date.issued2012-04en
dc.identifier.citationCopeland DM (2012) A negative-norm least-squares method for time-harmonic Maxwell equations. Journal of Mathematical Analysis and Applications 388: 303–317. Available: http://dx.doi.org/10.1016/j.jmaa.2011.09.004.en
dc.identifier.issn0022-247Xen
dc.identifier.doi10.1016/j.jmaa.2011.09.004en
dc.identifier.urihttp://hdl.handle.net/10754/597332en
dc.description.abstractThis 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.en
dc.description.sponsorshipThe 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).en
dc.publisherElsevier BVen
dc.subjectAxisymmetryen
dc.subjectFinite elementen
dc.subjectLeast squaresen
dc.subjectMaxwell equationsen
dc.subjectWeighted Sobolev spaceen
dc.titleA negative-norm least-squares method for time-harmonic Maxwell equationsen
dc.typeArticleen
dc.identifier.journalJournal of Mathematical Analysis and Applicationsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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