论文标题
分析混合不连续的Galerkin方法，用于具有最小平滑性要求的时谐麦克斯韦方程
Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements
论文作者
论文摘要
提出了对具有最小平滑度要求的时谐波麦克斯韦方程的混合不连续galerkin（DG）方法的误差分析。 DG方法的误差分析的关键难度是，精确解决方案的切向或正常轨迹在计算网格的网格面上未明确定义。我们通过两个步骤克服了这一困难。首先，我们采用起重操作员来替换网格面上的切向/正常迹线的积分，并通过音量积分来替换网格面上的痕迹。其次，通过使用平滑的插值来证明最佳的收敛速率，这些插值仅适用于仅用于集成功能的明确定义。作为我们分析的副产品，给出了明确且易于计算的稳定参数。
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.
