Optimal error estimates for Nedelec edge elements for time-harmonic Maxwell's equations

Abstract

In this paper, we obtain optimal error estimates in both L2-norm and H(curl)-norm for the Nedelec 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 L2 error estimates into the L2 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. Copyright 2009 by AMSS, Chinese Academy of Sciences.