@Article{JCM-27-563,
author = {Liuqiang Zhong, Shi Shu, Gabriel Wittum and Jinchao Xu},
title = {Optimal Error Estimates for Nédélec Edge Elements for Time-Harmonic Maxwell's Equations},
journal = {Journal of Computational Mathematics},
year = {2009},
volume = {27},
number = {5},
pages = {563--572},
abstract = {<p style="text-align: justify;">In this paper, we obtain optimal error estimates in both $L^2$-norm and $\boldsymbol{H}$(<strong>curl</strong>)-norm for the Nédélec edge finite element approximation of the time-harmonic Maxwell&#39;s equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the $L^2$&nbsp;error estimates into the $L^2$&nbsp;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&#39;s second type elements, we present an optimal convergence estimate which improves the best results available in the literature.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2009.27.5.011},
url = {http://global-sci.org/intro/article_detail/jcm/8590.html}
}