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稳态Poisson-Nernst-Planck方程的残量型后验误差估计

本站小编 Free考研考试/2021-12-27

房明娟, 阳莺, 唐鸣
桂林电子科技大学数学与计算科学学院, 桂林 541004
收稿日期:2019-03-12发布日期:2021-02-04
通讯作者:阳莺, Email: yangying@lsec.cc.ac.cn

基金资助:国家自然科学基金(11561016,11701119,11771105);广西自然科学基金项目(2017GXNSFFA 198012,2017GXNSFFA198056,2020GXNSFAA159098);广西高校数据分析与计算重点实验室开放基金资助项目;湘潭大学科学工程计算与数值仿真湖南省重点实验室开放课题基金资助.

RESIDUAL-TYPE A POSTERIORI ERROR ESTIMATES FOR STEADY-STATE POISSON-NERNST-PLANCK EQUATIONS

Fang Mingjuan Yang Ying Tang Ming
School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
Received:2019-03-12Published:2021-02-04







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针对稳态的Poisson-Nernst-Planck方程研究了一种残量型的后验误差估计子, 对方程的两个解-浓度和电势, 都分别给出了上界和下界估计. 数值实验表明, 基于这种后验误差估计子构造的自适应有限元算法对于稳态的Poisson-Nernst-Planck方程是有效的.
MR(2010)主题分类:
65N30
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[1] Marcicki J, Conlisk A T and Rizzoni G. Comparison of limiting descriptions of the electrical double layer using a simplified lithium-ion battery model[J]. ECS Transactions, 2012, 41(14):9-21.
[2] Ciucci F. Derivation of Micro/Macro Lithium Battery Models from Homogenization[J]. Transport in Porous Media, 2011, 88(2):249-270.
[3] Richardson G and King J R. Time-dependent modelling and asymptotic analysis of electrochemical cells[J]. Journal of Engineering Mathematics, 2007, 59(3):239-275.
[4] Jerome J. Analysis of Charge Transport:A mathematical theory and approximation of semiconductor models[M]. Springer-Verlag, New York, 1996.
[5] Bolintineanu D S, Sayyed-Ahmad A, Davis H T and Kaznessis Y N. Poisson-Nernst-Planck Models of Nonequilibrium Ion Electrodiffusion through a Protegrin Transmembrane Pore[J]. Plos Computational Biology, 2009, 5(1):e1000277.
[6] Lu B, Zhou Y, Huber, G A, Bond S D, Holst M J and McCammon J A. Electrodiffusion:a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution[J]. Journal of Chemical Physics, 2007, 127(13):135102.
[7] Singer A and Norbury J. Singer. A poisson-nernst-planck model for biological ion channels an asymptotic analysis in a three-dimensional narrow funnel[J]. Siam Journal on Applied Mathematics, 2009, 70(3):949-968.
[8] Cárdenas A E, Coalson R D and Kurnikova M G. Three-dimensional Poisson-Nernst-Planck theory studies:influence of membrane electrostatics on gramicidin A channel conductance[J]. Biophysical Journal, 2000, 79(1):80-93.
[9] Lu B, Holst M, McCammon J and Zhou Y C. Poisson-Nernst-Planck eauations for simulating biomolecular diffusion-reaction process I:Finite element solutions[J]. Journal of Computational Physics, 2010, 229(19):6979-6994.
[10] Zhou Y C, Lu B Z, Huber G A, Holst M J and McCammon J. A. Continuum simulations of acetylcholine consumption by acetylcholinesterase:a Poisson-Nernst-Planck approach[J]. Journal of Physical Chemistry B, 2008, 112(2):270-275.
[11] Lu B, Zhou Y. Poisson-Nernst-Planck equations for simulating biomolecular diffffusion-reaction processes II:size effffects on ionic distributions and diffffusion-reaction rates[J]. Biophysical Journal, 2011, 100(10):2475-2485.
[12] Lu B, Zhou Y C, Huber G A and Bond S D. Electrodiffusion:a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution[J]. Journal of Chemical Physics, 2007, 127(13):10B604-78.
[13] Tu B, Chen M, Xie Y, Zhang L, Eisenberg B and Lu B. A parallel finite element simulator for ion transport through three-dimensional ion channel systems[J]. Journal of Computational Chemistry, 2013, 34(24):2065-2078.
[14] Xie Y, Cheng J and Lu B, Zhang L B. Parallel adaptive finite element algorithms for solving the coupled electro-diffusion equation[J]. Molecular Based Mathematical Biology, 2013, 1:90-108.
[15] Sun Y Z, Sun P T, Zheng B and Lin G. Error a-nalysis of finite element method for PoissonNernst-Planck equations[J]. Journal of Computational and Applied Mathematics, 2016, 301:28-43.
[16] Yang Y and Zhou A H. Local averaging based a posteriori finite element error control for quasilinear elliptic problems with application to electrical potential computation[J]. Computer Methods in Applied Mechanics Engineering, 2006, 196(1):452-465.
[17] Brandts J and KŘÍŽEK M. Gradient superconvergence on uniform simplicial partitions of polytopes[J]. IMA Journal of Numerical Analysis, 2003, 23(3):489-505.
[18] Brenner S C and Scott L R. The Mathematical Theory of Finite Element Methods[M]. SpringerVerlag, New York, 1994.
[19] Shen R, Shu S, Yang Y and Lu B. A Decoupling Two-grid Method for the Time-dependent Poisson-Nernst-Planck Equations[J]. Numerical Algorithms, https://doi.org/10.1007/s11075-019-00744-4, 2019.
[20] Yang Y and Lu B Z. An error analysis for the finite element approximation to the steadystate Poisson-Nernst-Planck equations[J]. Advances in Applied Mathematics and Mechanics, 2013, 5(01):113-130.
[21] Verfurth R. A posteriori error estimators for convection-diffusion equations[J]. Numeriche Mathematik, 1998, 80:641-663.
[22] Verfurth R. A Review of a Posteriori Error Estimates and Adaptive Mesh-refinement Techniques[M]. Wiley-Teubner, New York, 1996.

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