Residual Type a Posteriori Error Estimates for the Time-Dependent Poisson–Nernst–Planck Equations

[1]  Zhaojie Zhou,et al.  A posteriori error estimates of constrained optimal control problem governed by convection diffusion equations , 2008 .

[2]  Marco Picasso,et al.  An adaptive algorithm for the Crank-Nicolson scheme applied to a time-dependent convection-diffusion problem , 2009, J. Comput. Appl. Math..

[3]  Benzhuo Lu,et al.  Superconvergent gradient recovery for nonlinear Poisson-Nernst-Planck equations with applications to the ion channel problem , 2020, Advances in Computational Mathematics.

[4]  Yiannis N. Kaznessis,et al.  Poisson-Nernst-Planck Models of Nonequilibrium Ion Electrodiffusion through a Protegrin Transmembrane Pore , 2009, PLoS Comput. Biol..

[5]  Minxin Chen,et al.  A parallel finite element simulator for ion transport through three‐dimensional ion channel systems , 2013, J. Comput. Chem..

[6]  Huadong Gao,et al.  Linearized Conservative Finite Element Methods for the Nernst–Planck–Poisson Equations , 2017, J. Sci. Comput..

[7]  Franco Brezzi,et al.  Numerical simulation of semiconductor devices , 1989 .

[8]  Dietrich Braess,et al.  Equilibrated residual error estimates are p-robust , 2009 .

[9]  M. Planck,et al.  Ueber die Erregung von Electricität und Wärme in Electrolyten , 1890 .

[10]  Benzhuo Lu,et al.  An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations , 2013 .

[11]  Wei Lai,et al.  Derivation of Micro/Macro Lithium Battery Models from Homogenization , 2011 .

[12]  J. Jerome.  Analysis of Charge Transport , 1996 .

[13]  Rüdiger Verfürth,et al.  A Posteriori Error Estimation Techniques for Finite Element Methods , 2013 .

[14]  Bob Eisenberg,et al.  A conservative finite difference scheme for Poisson–Nernst–Planck equations , 2013, Journal of Computational Electronics.

[15]  Hailiang Liu,et al.  A free energy satisfying finite difference method for Poisson-Nernst-Planck equations , 2013, J. Comput. Phys..

[16]  Bin Zheng,et al.  Error analysis of finite element method for Poisson-Nernst-Planck equations , 2016, J. Comput. Appl. Math..

[17]  Amit Singer,et al.  A Poisson--Nernst--Planck Model for Biological Ion Channels---An Asymptotic Analysis in a Three-Dimensional Narrow Funnel , 2009, SIAM J. Appl. Math..

[18]  Ivo Babuška,et al.  Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements , 1992 .

[19]  Xiu Ye,et al.  A posterior error estimate for finite volume methods of the second order elliptic problem , 2011 .

[20]  J. Oden,et al.  A Posteriori Error Estimation in Finite Element Analysis: Oden/A Posteriori , 2000 .

[21]  Cheng Wang,et al.  A Posteriori Error Estimates of Two-Grid Finite Element Methods for Nonlinear Elliptic Problems , 2018, J. Sci. Comput..

[22]  W. Nernst,et al.  Die elektromotorische Wirksamkeit der Jonen , 1889 .

[23]  John R. King,et al.  Time-dependent modelling and asymptotic analysis of electrochemical cells , 2007 .

[24]  Michael J. Holst,et al.  Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions , 2010, J. Comput. Phys..

[25]  Pablo Venegas,et al.  An a posteriori error estimator for an unsteady advection-diffusion-reaction problem , 2014, Comput. Math. Appl..

[26]  Fabio Nobile,et al.  A posteriori error estimation for elliptic partial differential equations with small uncertainties , 2016 .

[27]  Sanjay R. Mathur,et al.  A multigrid method for the Poisson–Nernst–Planck equations , 2009 .

[28]  A. T. Conlisk,et al.  Comparison of Limiting Descriptions of the Electrical Double Layer Using a Simplified Lithium-Ion Battery Model , 2012 .

[29]  Rüdiger Verfürth,et al.  A posteriori error estimates for finite element discretizations of the heat equation , 2003 .

[30]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[31]  Barry Honig,et al.  Extending the Applicability of the Nonlinear Poisson−Boltzmann Equation: Multiple Dielectric Constants and Multivalent Ions† , 2001 .

[32]  Aihui Zhou,et al.  Local averaging based a posteriori finite element error control for quasilinear elliptic problems with application to electrical potential computation , 2006 .

[33]  C. Makridakis,et al.  A posteriori error estimates for fully discrete schemes for the time dependent Stokes problem , 2018 .

[34]  Claire Chainais-Hillairet,et al.  Study of a Finite Volume Scheme for the Drift-Diffusion System. Asymptotic Behavior in the Quasi-Neutral Limit , 2013, SIAM J. Numer. Anal..