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 $\bfH(\curl)$-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.
翻译:开发了一种虚拟元素方法(VEM),该方法具有第一级最佳汇合顺序,用于解决一个特殊类别的多边形网格的二维 Maxwell 界面问题,该界面从一个不适宜网格的背景中切除。在符合最大角条件的多边形网格的虚拟三角图上引入了一个新的虚拟空间,该边框与通常的 $\bfH(\curl) 和$(curl) 相匹配的虚拟空间有着完全相同的自由度。这个新的虚拟空间是证明 VEM 的最佳误差界限独立于界面附近可能存在的厌异多边网格网格的高方位比例的关键。