Error Analysis of Virtual Element Methods for the Time-dependent Poisson-Nernst-Planck Equations
Numerical Analysis
2022-07-18 v1 Numerical Analysis
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 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 and norms. Finally, a numerical experiment verifies the theoretical convergence results.
Cite
@article{arxiv.2207.07231,
title = {Error Analysis of Virtual Element Methods for the Time-dependent Poisson-Nernst-Planck Equations},
author = {Ying Yang and Ya Liu and Shi Shu},
journal= {arXiv preprint arXiv:2207.07231},
year = {2022}
}