We present a low order virtual element discretization for time dependent Maxwell's equations, which allow for the use of general polyhedral meshes. Both the semi- and fully-discrete schemes are considered. We derive optimal a priori estimates and validate them on a set of numerical experiments. As pivot results, we discuss some novel inequalities associated with de Rahm sequences of nodal, edge, and face virtual element spaces.

中文翻译：

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麦克斯韦方程组的虚拟元素

我们为时间相关的麦克斯韦方程提供了低阶虚拟元素离散化，它允许使用一般的多面体网格。考虑了半离散和全离散方案。我们推导出最佳先验估计并在一组数值实验中验证它们。作为枢轴结果，我们讨论了与节点、边缘和面虚拟元素空间的 de Rahm 序列相关的一些新的不等式。