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

07/14/2022

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by   Ying Yang, et al.

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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.