We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck equations, which are a nonlinear coupled system widely used in semiconductors and ion channels. The spatial discretization is based on the elliptic projection and the $L^2$ projection operator, and for the temporal discretization, the backward Euler scheme is employed. After presenting the semi and fully discrete schemes, we derive the a priori error estimates in the $L^2$ and $H^1$ norms. Finally, a numerical experiment verifies the theoretical convergence results.

翻译：我们讨论并分析用于具有时间依赖性的Poisson-Nernst-Planck等式的普通多边形网球的虚拟元素方法,这是在半导体和离子信道中广泛使用的非线性连接系统,空间离散以椭圆投影和2美元投影操作员为基础,对于时间离散,则采用落后的Euler方案。在提出半离子方案后,我们得出了先验误差估计数,分别是$L$2和$H$1。最后,一个数字实验可以核实理论趋同的结果。