A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system

DOI10.1090/mcom/3642zbMath1480.65213arXiv2009.08076OpenAlexW3133356548MaRDI QIDQ4999469

Chun Liu, Shenggao Zhou, Cheng Wang, Xing Ye Yue, Steven M. Wise

Publication date: 7 July 2021

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.08076

zbMATH Keywords

energy stabilitypositivity preservingPoisson-Nernst-Planck (PNP) systemoptimal rate convergence analysishigher order asymptotic expansionlogarithmic energy potential

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonlinear parabolic equations (35K55) PDEs in connection with optics and electromagnetic theory (35Q60) Initial-boundary value problems for higher-order parabolic equations (35K35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Asymptotic expansions of solutions to PDEs (35C20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Positive solutions to PDEs (35B09) Electrochemistry (78A57)

Related Items (33)

A Thermodynamically-Consistent Phase Field Crystal Model of Solidification with Heat Flux ⋮ A Structure-Preserving JKO Scheme for the SizeModified Poisson-Nernst-Planck-Cahn-Hilliard Equations ⋮ A positivity-preserving, energy stable scheme for a ternary Cahn-Hilliard system with the singular interfacial parameters ⋮ A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance ⋮ SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions ⋮ Linear-scaling selected inversion based on hierarchical interpolative factorization for self Green's function for modified Poisson-Boltzmann equation in two dimensions ⋮ High-order space-time finite element methods for the Poisson-Nernst-Planck equations: positivity and unconditional energy stability ⋮ A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation ⋮ Unconditionally energy stable and bound-preserving schemes for phase-field surfactant model with moving contact lines ⋮ A positivity preserving, energy stable finite difference scheme for the Flory-Huggins-Cahn-Hilliard-Navier-Stokes system ⋮ A Modified Crank-Nicolson Numerical Scheme for the Flory-Huggins Cahn-Hilliard Model ⋮ Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance ⋮ Optimal rate convergence analysis of a numerical scheme for the ternary Cahn-Hilliard system with a Flory-Huggins-deGennes energy potential ⋮ A Second-Order Accurate, Operator Splitting Scheme for Reaction-Diffusion Systems in an Energetic Variational Formulation ⋮ A Maxwell–Ampère Nernst–Planck Framework for Modeling Charge Dynamics ⋮ EnVarA-FEM for the flux-limited porous medium equation ⋮ Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes ⋮ A positivity-preserving and convergent numerical scheme for the binary fluid-surfactant system ⋮ A second order accurate, positivity preserving numerical method for the Poisson-Nernst-Planck system and its convergence analysis ⋮ A uniquely solvable, positivity-preserving and unconditionally energy stable numerical scheme for the functionalized Cahn-Hilliard equation with logarithmic potential ⋮ Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model ⋮ Error estimates for the finite element method of the Navier-Stokes-Poisson-Nernst-Planck equations ⋮ Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation ⋮ Convergence analysis of structure‐preserving numerical methods for nonlinear Fokker–Planck equations with nonlocal interactions ⋮ A positivity-preserving, energy stable BDF2 scheme with variable steps for the Cahn-Hilliard equation with logarithmic potential ⋮ Energy dissipative and positivity preserving schemes for large-convection ion transport with steric and solvation effects ⋮ Efficient time-stepping schemes for the Navier-Stokes-Nernst-Planck-Poisson equations ⋮ A BDF2 energy‐stable scheme for the binary fluid‐surfactant hydrodynamic model ⋮ Unnamed Item ⋮ A positivity-preserving and free energy dissipative hybrid scheme for the Poisson-Nernst-Planck equations on polygonal and polyhedral meshes ⋮ An iteration solver for the Poisson-Nernst-Planck system and its convergence analysis ⋮ A dynamic mass transport method for Poisson-Nernst-Planck equations ⋮ A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An \(H^2\) convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn-Hilliard equation
• A free energy satisfying finite difference method for Poisson-Nernst-Planck equations
• A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation
• An energy-conserving second order numerical scheme for nonlinear hyperbolic equation with an exponential nonlinear term
• Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations
• The Cahn-Hilliard equation with logarithmic potentials
• A conservative discretization of the Poisson-Nernst-Planck equations on adaptive Cartesian grids
• Energetically stable discretizations for charge transport and electrokinetic models
• Convergent discretizations for the Nernst-Planck-Poisson system
• Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation
• A modified Poisson-Nernst-Planck model with excluded volume effect: theory and numerical implementation
• A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems
• An energy preserving finite difference scheme for the Poisson-Nernst-Planck system
• Analysis of a fourth-order finite difference method for the incompressible Boussinesq equations
• On a phase-field model with a logarithmic nonlinearity.
• Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems
• Structure-preserving and efficient numerical methods for ion transport
• A positive and energy stable numerical scheme for the Poisson-Nernst-Planck-Cahn-Hilliard equations with steric interactions
• A fully discrete positivity-preserving and energy-dissipative finite difference scheme for Poisson-Nernst-Planck equations
• Positivity preserving finite difference methods for Poisson-Nernst-Planck equations with steric interactions: application to slit-shaped nanopore conductance
• A positivity-preserving, energy stable and convergent numerical scheme for the Cahn-Hilliard equation with a Flory-Huggins-deGennes energy
• A positivity preserving and free energy dissipative difference scheme for the Poisson-Nernst-Planck system
• Linearized conservative finite element methods for the Nernst-Planck-Poisson equations
• A fourth-order numerical method for the planetary geostrophic equations with inviscid geostrophic balance
• Projection method III: Spatial discretization on the staggered grid
• Adiabatic Relaxation of Convective-Diffusive Gas Transport in a Porous Fuel Cell Electrode
• Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation
• An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation
• Convergence analysis for second-order accurate schemes for the periodic nonlocal Allen-Cahn and Cahn-Hilliard equations
• An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
• Surface Pressure Poisson Equation Formulation of the Primitive Equations: Numerical Schemes
• Convergence of gauge method for incompressible flow
• Nonlinear Smoluchowski slip velocity and micro-vortex generation
• The Cahn–Hilliard–Oono equation with singular potential
• Projection Method I: Convergence and Numerical Boundary Layers
• Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn–Hilliard equation
• Convergence Analysis of a Numerical Scheme for the Porous Medium Equation by an Energetic Variational Approach
• Unconditional Positivity-Preserving and Energy StableSchemesforaReducedPoisson-Nernst-Planck System
• A Positivity-Preserving Second-Order BDF Scheme for the Cahn-Hilliard Equation with Variable Interfacial Parameters
• Optimal Rate Convergence Analysis of a Second Order Numerical Scheme for the Poisson--Nernst--Planck System
• Modeling and simulating asymmetrical conductance changes in gramicidin pores
• Error analysis of finite element method for Poisson-Nernst-Planck equations
• Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential

This page was built for publication: A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system