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

Dylan M. Copeland

Research output: Contribution to journalArticlepeer-review

2 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 languageEnglish (US)
Pages (from-to)303-317
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume388
Issue number1
DOIs
StatePublished - Apr 2012
Externally publishedYes

Bibliographical 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.

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