An error analysis of a mixed discontinuous Galerkin (DG) method with Brezzi numerical flux for the time-harmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method is that the tangential or normal trace of the exact solution is not well-defined on the mesh faces of the computational mesh. We overcome this difficulty by two steps. First, we employ a lifting operator to replace the integrals of the tangential/normal traces on mesh faces by volume integrals. Second, optimal convergence rates are proven by using smoothed interpolations that are well-defined for merely integrable functions. As a byproduct of our analysis, an explicit and easily computable stabilization parameter is given.

中文翻译：

---

具有最小平滑度要求的时谐麦克斯韦方程的混合不连续伽辽金方法分析

对具有最小平滑度要求的时谐麦克斯韦方程组的 Brezzi 数值通量的混合不连续伽辽金 (DG) 方法进行了误差分析。DG 方法误差分析的主要困难在于精确解的切线或法线轨迹在计算网格的网格面上没有明确定义。我们通过两个步骤克服了这个困难。首先，我们使用提升算子将网格面上的切线/法线轨迹的积分替换为体积积分。其次，通过使用仅针对可积函数定义良好的平滑插值来证明最佳收敛速度。作为我们分析的副产品，给出了一个明确且易于计算的稳定参数。