We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing rules were reported, which guarantee the convergence of finite element approximations to the related scalar source problems. Here we generalize these results to the electromagnetic two dimensional vectorial equations and the related holomorphic eigenvalue problems. Different than for the analysis on the continuous level, we require an assumption on both contrasts of the permittivity and the permeability. We confirm our theoretical results with computational studies.

翻译：我们考虑的是由古典物质环绕的分散材料合成物中的时间-调和电磁波方程式。在某些频率范围内,这会导致信号改变允许性和/或渗透性。以前曾报告过网状规则,保证了有限元素近似与相关天平源问题的趋同。我们在这里将这些结果归纳为电磁二维矢量方程式和相关的天体天文值问题。不同于对连续水平的分析,我们要求对许可性和渗透性两者的对比进行假设。我们用计算研究来证实我们的理论结果。