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arXiv · 2207.07231

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

Ying Yang·Ya Liu·Shi Shu
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Abstract

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.

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Ying Yang, Ya Liu, Shi Shu. 2022-07-14. Error Analysis of Virtual Element Methods for the Time-dependent Poisson-Nernst-Planck Equations. https://arxiv.org/abs/2207.07231

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