Preasymptotic error estimates of higher-order EEM for the time-harmonic Maxwell equations with large wave number

The time-harmonic Maxwell equations with impedance boundary condition and large wave number are discretized using the second-type Nédélec’s edge element method (EEM). Preasymptotic error bounds are derived, showing that, under the mesh condition ${\kappa }^{2p+1}{h}^{2p}$ being sufficiently small, the error of the EEM of order $p$ in the energy norm is bounded by $\mathcal{O}({\kappa }^p{h}^p+{\kappa }^{2p+1}{h}^{2p})$, while the error in the $\kappa$-scaled ${\mathit{L}}^2$ norm is bounded by $\mathcal{O}((\kappa h{)}^{p+1}+{\kappa }^{2p+1}{h}^{2p})$. Here, $\kappa$ is the wave number and $h$ is the mesh size. Numerical tests are provided to illustrate our theoretical results.