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Finite Element Methods for Maxwell's Equations$
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Peter Monk

Print publication date: 2003

Print ISBN-13: 9780198508885

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198508885.001.0001

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Topics Concerning Finite Elements

Topics Concerning Finite Elements

(p.199) 8 Topics Concerning Finite Elements
Finite Element Methods for Maxwell's Equations

Peter Monk

Oxford University Press

Besides the first family of edge elements discussed in Chapter 5, there is a second family of elements of full polynomial degree at each order, also due to Nedelec. These have the potential advantage of a higher convergence rate in the least squares norm compared to the curl norm. This chapter defines and analyses these elements, followed by a discussion of curved domains. Edge elements in this setting are by no means well understood, but in the case of refined block structured grids based on mapping, the analysis of the previous chapters is relevant. Lastly, hp-finite element methods for Maxwell’s equations are introduced.

Keywords:   second family of elements, edge elements, curved domain, hp-finite elements

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