论文标题
在最低规律性下，无限期谐波麦克斯韦方程的HDG和CG方法
HDG and CG methods for the Indefinite Time-Harmonic Maxwell's Equations under minimal regularity
论文作者
论文摘要
我们建议使用连续盖尔金（CG）方法结合使用杂交的不连续的Galerkin（HDG）方法来近似Maxwell的方程。我们在本文中做出了两项贡献。首先，即使有许多论文使用HDG方法来近似Maxwell的方程，据我们所知，他们都认为系数是光滑的（或恒定）。在这里，当电磁系数是{\ em零件}平滑时，我们得出了HGD-CG近似的最佳收敛估计。这需要新的分析技术。其次，我们使用CG元素来近似用于强制差异条件的Lagrange乘法器，并获得了一个离散系统，可以使我们可以将离散的Lagrange乘数分离。因为我们使用的是连续的Lagrange乘数空间，所以专用于此的自由度的数量小于其他HDG方法。我们提出数值实验以确认我们的理论结果。
We propose to use a hybridizable discontinuous Galerkin (HDG) method combined with the continuous Galerkin (CG) method to approximate Maxwell's equations. We make two contributions in this paper. First, even though there are many papers using HDG methods to approximate Maxwell's equations, to our knowledge they all assume that the coefficients are smooth (or constant). Here, we derive optimal convergence estimates for our HGD-CG approximation when the electromagnetic coefficients are {\em piecewise} smooth. This requires new techniques of analysis. Second, we use CG elements to approximate the Lagrange multiplier used to enforce the divergence condition and we obtain a discrete system in which we can decouple the discrete the Lagrange multiplier. Because we are using a continuous Lagrange multiplier space, the number of degrees of freedom devoted to this are less than for other HDG methods. We present numerical experiments to confirm our theoretical results.
