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Numerical Algorithms
Published in: Numerical Algorithms 4/2020

07-06-2019 | Original Paper

A decoupling two-grid method for the time-dependent Poisson-Nernst-Planck equations

Authors: Ruigang Shen, Shi Shu, Ying Yang, Benzhuo Lu

Published in: Numerical Algorithms | Issue 4/2020

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Abstract

We study a two-grid strategy for decoupling the time-dependent Poisson-Nernst-Planck equations describing the mass concentration of ions and the electrostatic potential. The computational system is decoupled to smaller systems by using coarse space solutions at each time level, which can speed up the solution process compared with the finite element method combined with the Gummel iteration. We derive the optimal error estimates in L2 norm for both semi- and fully discrete finite element approximations. Based on the a priori error estimates, the error estimates in H1 norm are presented for the two-grid algorithm. The theoretical results indicate this decoupling method can retain the same accuracy as the finite element method. Numerical experiments including the Poisson-Nernst-Planck equations for an ion channel show the efficiency and effectiveness of the decoupling two-grid method.
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Metadata
Title
A decoupling two-grid method for the time-dependent Poisson-Nernst-Planck equations
Authors
Ruigang Shen
Shi Shu
Ying Yang
Benzhuo Lu
Publication date
07-06-2019
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00744-4

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