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.

翻译：针对大波数时谐Maxwell方程，本文推导了线性边元法（EEM）及线性$\boldsymbol{H}(\boldsymbol{\mathrm{curl}})$-协调内部惩罚边元法（CIP-EEM）的渐近前误差估计。研究表明，在满足网格条件$\kappa^3 h^2$充分小时，两种方法所得解在能量范数下的误差界为$\mathcal{O} (\kappa h + \kappa^3 h^2 )$，在$\boldsymbol{L}^2$范数下的误差界为$\mathcal{O} (\kappa h^2 + \kappa^2 h^2 )$，其中$\kappa$为波数，$h$为网格尺寸。数值实验验证了理论结果，并表明CIP-EEM具有显著减小污染效应的潜力。