A Decoupling Two-Grid Method for the Steady-State Poisson-Nernst-Planck Equations

Author(s)

    Ying Yang
    School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China
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,
    Benzhuo Lu
    LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, the National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
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    Yan Xie
    LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
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Abstract

Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck equations by coarse grid finite element approximations. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid algorithms for solving Poisson-Nernst-Planck equations.

Keywords:

Poisson-Nernst-Planck equations Two-grid finite element method Decoupling method Error analysis Gummel iteration.
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DOI

10.4208/jcm.1904-m2018-0181

How to Cite

A Decoupling Two-Grid Method for the Steady-State Poisson-Nernst-Planck Equations. (2019). Journal of Computational Mathematics, 37(4), 556-578. https://doi.org/10.4208/jcm.1904-m2018-0181