不定时谐Maxwell方程的可杂交间断Galerkin方法
A hybridizable discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations
中文总结 AI 辅助
本文针对三维不定时谐Maxwell方程提出可杂交间断Galerkin方法，通过波数显式正则性分析和离散inf-sup条件证明，建立了与波数无关的最优阶误差估计，并用数值实验验证了理论结果。
中文摘要 AI 辅助
本文旨在为三维空间中具有完美导电边界的不定时谐Maxwell方程发展一种可杂交间断Galerkin（HDG）方法。首先，我们推导了波数显式正则性结果，该结果在HDG方法的误差分析中起着重要作用。其次，我们证明了一个离散inf-sup条件，该条件对所有正网格尺寸h、所有波数k以及一般区域Ω均成立。然后，我们建立了所研究HDG方法的最优阶误差估计，其中的常数与波数无关。理论结果通过数值实验得到了验证。
英文摘要
In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary in the three-dimensional space. First, we derive the wavenumber explicit regularity result, which plays an important role in the error analysis for the HDG method. Second, we prove a discrete inf-sup condition which holds for all positive mesh size $h$, for all wavenumber $k$, and for general domain $Ω$. Then, we establish the optimal order error estimates of the underlying HDG method with constant independent of the wavenumber. The theoretical results are confirmed by numerical experiments.
