TY - JOUR
T1 - Optimal Error Estimates for Nédélec Edge Elements for Time-Harmonic Maxwell's Equations
AU - Liuqiang Zhong, Shi Shu, Gabriel Wittum & Jinchao Xu
JO - Journal of Computational Mathematics
VL - 5
SP - 563
EP - 572
PY - 2009
DA - 2009/10
SN - 27
DO - http://doi.org/10.4208/jcm.2009.27.5.011
UR - https://global-sci.org/intro/article_detail/jcm/8590.html
KW - Edge finite element, Time-harmonic Maxwell's equations.
AB - <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>