Preasymptotic error estimates of EEM and CIP-EEM for the time-harmonic Maxwell equations with large wave number
<|reference_start|>Preasymptotic error estimates of EEM and CIP-EEM for the time-harmonic Maxwell equations with large wave number: Preasymptotic error estimates are derived for the linear edge element method (EEM) and the linear $\boldsymbol{H}(\boldsymbol{\mathrm{curl}})$-conforming interior penalty edge element method (CIP-EEM) for the time-harmonic Maxwell equations with large wave number. It is shown that under the mesh condition that $\kappa^3 h^2$ is sufficiently small, the errors of the solutions to both methods are bounded by $\mathcal{O} (\kappa h + \kappa^3 h^2 )$ in the energy norm and $\mathcal{O} (\kappa h^2 + \kappa^2 h^2 )$ in the $\boldsymbol{L}^2$ norm, where $\kappa$ is the wave number and $h$ is the mesh size. Numerical tests are provided to verify our theoretical results and to illustrate the potential of CIP-EEM in significantly reducing the pollution effect.<|reference_end|>
@article{lu2024preasymptotic,
    title={Preasymptotic error estimates of EEM and CIP-EEM for the time-harmonic
  Maxwell equations with large wave number},
    author={Shuaishuai Lu, Haijun Wu},
    journal={arXiv preprint arXiv:2407.06784},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.06784},
    primaryClass={math.NA cs.NA}
}