A virtual element method (VEM) with the first-order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background unfitted mesh. A novel virtual space is introduced on a virtual triangulation of the polygonal mesh satisfying a maximum angle condition, which shares exactly the same degrees of freedom as the usual H(curl)-conforming virtual space. This new virtual space serves as the key to prove that the optimal error bounds of the VEM are independent of high aspect ratio of the possible anisotropic polygonal mesh near the interface.

中文翻译：

---

具有背景未拟合网格的二维麦克斯韦界面问题的虚拟有限元方法

开发了一种具有一阶最优收敛阶的虚拟单元法 (VEM)，用于解决一类特殊多边形网格上的二维 Maxwell 界面问题，该多边形网格由界面从背景未拟合网格中切割出来。在满足最大角度条件的多边形网格的虚拟三角剖分上引入了一种新颖的虚拟空间，该虚拟空间与通常的自由度完全相同H(卷曲)- 符合虚拟空间。这个新的虚拟空间是证明 VEM 的最佳误差界限与界面附近可能的各向异性多边形网格的高纵横比无关的关键。