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We discuss and analyze the virtual element method on general polygonal meshesfor the time-dependent Poisson-Nernst-Planck equations, which are a nonlinearcoupled system widely used in semiconductors and ion channels. The spatialdiscretization is based on the elliptic projection and the $L^2$ projectionoperator, and for the temporal discretization, the backward Euler scheme isemployed. After presenting the semi and fully discrete schemes, we derive the apriori error estimates in the $L^2$ and $H^1$ norms. Finally, a numericalexperiment verifies the theoretical convergence results.

Error Analysis of Virtual Element Methods for the Time-dependent Poisson-Nernst-Planck Equations