Journals
Resources
About Us
Open Access

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

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

Year:    2025

Author:    Ying Yang, Ya Liu, Yang Liu, Shi Shu

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 731–770

Abstract

We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck (PNP) equations, which are a nonlinear coupled system widely used in semiconductors and ion channels. After presenting the semi-discrete scheme, the optimal $H^1$ norm error estimates are presented for the time-dependent PNP equations, which are based on some error estimates of a virtual element energy projection. The Gummel iteration is used to decouple and linearize the PNP equations and the error analysis is also given for the iteration of fully discrete virtual element approximation. The numerical experiment on different polygonal meshes verifies the theoretical convergence results and shows the efficiency of the virtual element method.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2401-m2023-0130

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 731–770

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    40

Keywords:    Virtual element method Error estimate Poisson-Nernst-Planck equations Polygonal meshes Energy projection Gummel iteration.

Author Details

Ying Yang

Ya Liu

Yang Liu

Shi Shu