A conforming virtual element method is studied for approximating the solution of a pulsed electric interface model on polygonal meshes with small edges or faces, which traditional virtual and finite element methods cannot easily handle. One of the significant advantages of this virtual element method is to generate interface-conforming meshes efficiently exploiting polygonal meshes and hanging nodes. The virtual element method employs specific projection operators to establish optimal error estimates with reasonable assumptions regarding the solution's regularity. The voltage potential of the pulsed electric model through the physical media is approximated by using a fully discrete virtual element approach based on Crank-Nicolson temporal discretization. Numerical examples are used to illustrate the expected order of convergence. The efficiency and robustness of the proposed method are displayed on interface-independent/dependent background-fitted meshes with small edges and large magnitudes of discontinuities across the interface by these experiments.

中文翻译：

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小边多边形网格电接口模型虚拟元法收敛性分析

研究了一种一致的虚拟元方法，用于逼近具有小边或面的多边形网格上的脉冲电界面模型的解，这是传统虚拟和有限元方法无法轻松处理的。这种虚拟元素方法的显着优点之一是有效地利用多边形网格和悬挂节点生成符合界面的网格。虚拟元素方法采用特定的投影算子，通过对解的规律性的合理假设来建立最佳误差估计。通过使用基于 Crank-Nicolson 时间离散化的完全离散虚拟元件方法来近似通过物理介质的脉冲电模型的电压电势。数值例子用于说明预期的收敛顺序。通过这些实验，所提出方法的效率和鲁棒性显示在与界面无关/相关的背景拟合网格上，这些网格具有小边缘和界面上的大量不连续性。