An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations

被引：36
|
作者：
Yang, Ying [1 ]
Lu, Benzhuo [2 ]
机构：
[1] Guilin Univ Elect Technol, Dept Computat Sci & Math, Guilin 541004, Guangxi, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Natl Ctr Math & Interdisciplinary Sci,LSEC, Beijing 100190, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2013年 / 5卷 / 01期
关键词：
Poisson-Nernst-Planck equations; finite element method; error bounds; ELECTROSTATIC POTENTIAL COMPUTATION; GREENS-FUNCTION APPROXIMATIONS; BOLTZMANN EQUATION; ACETYLCHOLINESTERASE; GRAMICIDIN; CHANNEL;
D O I：
10.4208/aamm.11-m11184
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources, which describe the electrodfffusion of ions in a solvated biomolecular system. In this paper, some error bounds for a piecewise finite element approximation to this problem are derived. Several numerical examples including biomolecular problems are shown to support our analysis.
引用
收藏
页码：113 / 130
页数：18
相关论文
共 50 条
  • [21] Qualitative properties of steady-state Poisson-Nernst-Planck systems: Mathematical study
    Park, JH
    Jerome, JW
    SIAM JOURNAL ON APPLIED MATHEMATICS, 1997, 57 (03) : 609 - 630
  • [22] ERROR ANALYSIS OF VIRTUAL ELEMENT METHODS FOR THE TIME-DEPENDENT POISSON-NERNST-PLANCK EQUATIONS
    Yang, Ying
    Liu, Ya
    Liu, Yang
    Shu, Shi
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2025, 43 (03): : 731 - 770
  • [23] Mixed finite element analysis for the Poisson-Nernst-Planck/Stokes coupling
    He, Mingyan
    Sun, Pengtao
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 341 : 61 - 79
  • [24] Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson-Nernst-Planck Equations
    Ding, Jie
    Sun, Hui
    Wang, Zhongming
    Zhou, Shenggao
    COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2018, 23 (05) : 1549 - 1572
  • [25] Singular perturbation analysis of the steady-state Poisson-Nernst-Planck system: Applications to ion channels
    Singer, A.
    Gillespie, D.
    Norbury, J.
    Eisenberg, R. S.
    EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2008, 19 : 541 - 560
  • [26] A conservative finite difference scheme for Poisson-Nernst-Planck equations
    Flavell, Allen
    Machen, Michael
    Eisenberg, Bob
    Kabre, Julienne
    Liu, Chun
    Li, Xiaofan
    JOURNAL OF COMPUTATIONAL ELECTRONICS, 2014, 13 (01) : 235 - 249
  • [27] Qualitative properties of steady-state Poisson-Nernst-Planck systems: Perturbation and simulation study
    Barcilon, V
    Chen, DP
    Eisenberg, RS
    Jerome, JW
    SIAM JOURNAL ON APPLIED MATHEMATICS, 1997, 57 (03) : 631 - 648
  • [28] Superconvergent estimate of a Galerkin finite element method for nonlinear Poisson-Nernst-Planck equations
    Shi, Xiangyu
    Lu, Linzhang
    APPLIED MATHEMATICS LETTERS, 2020, 104
  • [29] Unconditional superconvergence analysis of a structure-preserving finite element method for the Poisson-Nernst-Planck equations
    Yang, Huaijun
    Li, Meng
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2024, 50 (03)
  • [30] A multigrid method for the Poisson-Nernst-Planck equations
    Mathur, Sanjay R.
    Murthy, Jayathi Y.
    INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2009, 52 (17-18) : 4031 - 4039
12345