@Article{JCM-27-563, author = {}, 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 = {

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.

}, 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} }