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Optimal Error Estimates for Nédélec Edge Elements for Time-Harmonic Maxwell's Equations

Optimal Error Estimates for Nédélec Edge Elements for Time-Harmonic Maxwell's Equations
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Year:    2009

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 5 : pp. 563–572

Abstract

In this paper, we obtain optimal error estimates in both $L^2$-norm and $\boldsymbol{H}$(curl)-norm for the Nédélec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the $L^2$ error estimates into the $L^2$ estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nédélec's second type elements, we present an optimal convergence estimate which improves the best results available in the literature.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.27.5.011

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 5 : pp. 563–572

Published online:    2009-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Edge finite element Time-harmonic Maxwell's equations.

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