标题： 高频时谐Maxwell方程组大波数下高阶EEM的预渐近误差估计 显示英文标题

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

摘要： 时间谐振 Maxwell 方程组结合阻抗边界条件以及大波数情形下，采用第二类 Nedéléc 边缘元方法（EEM）进行离散化。推导了预渐近误差界，表明在网格满足条件$\kappa^{2p+1}h^{2p}$足够小时，能量范数下 EEM 的阶数$p$误差被界为$\mathcal{O}\big(\kappa^{p}h^p + \kappa^{2p+1}h^{2p}\big)$，而$\kappa$-缩放的$\boldsymbol{L}^2$范数下的误差被界为$\mathcal{O}\big((\kappa h)^{p+1} + \kappa^{2p+1} h^{2p}\big)$。 这里，$\kappa$是波数，$h$是网格尺寸。 提供了数值测试以说明我们的理论结果。 显示英文摘要

摘要： The time-harmonic Maxwell equations with impedance boundary condition and large wave number are discretized using the second-type N\'{e}d\'{e}lec'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 $\mathcal{O}\big(\kappa^{p}h^p + \kappa^{2p+1}h^{2p}\big)$, while the error in the $\kappa$-scaled $\boldsymbol{L}^2$ norm is bounded by $\mathcal{O}\big((\kappa h)^{p+1} + \kappa^{2p+1} h^{2p}\big)$. Here, $\kappa$ is the wave number and $h$ is the mesh size. Numerical tests are provided to illustrate our theoretical results.