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

C Liu, C Wang, S Wise, X Yue, S Zhou - Mathematics of Computation, 2021‏ - ams.org
In this paper we propose and analyze a finite difference numerical scheme for the Poisson-
Nernst-Planck equation (PNP) system. To understand the energy structure of the PNP …

Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions

W Cai, C Jiang, Y Wang, Y Song - Journal of Computational Physics, 2019‏ - Elsevier
This paper presents two kinds of strategies to construct structure-preserving algorithms with
homogeneous Neumann boundary conditions for the sine-Gordon equation, while most …

Unconditionally positivity preserving and energy dissipative schemes for Poisson–Nernst–Planck equations

J Shen, J Xu - Numerische Mathematik, 2021‏ - Springer
We develop a set of numerical schemes for the Poisson–Nernst–Planck equations. We
prove that our schemes are mass conservative, uniquely solvable and keep positivity …

Efficient, positive, and energy stable schemes for multi-D Poisson–Nernst–Planck systems

H Liu, W Maimaitiyiming - Journal of Scientific Computing, 2021‏ - Springer
In this paper, we design, analyze, and numerically validate positive and energy-dissipating
schemes for solving the time-dependent multi-dimensional system of Poisson–Nernst …

Positivity Preserving and Mass Conservative Projection Method for the Poisson–Nernst–Planck Equation

F Tong, Y Cai - SIAM Journal on Numerical Analysis, 2024‏ - SIAM
We propose and analyze a novel approach to construct structure preserving approximations
for the Poisson–Nernst–Planck equations, focusing on the positivity preserving and mass …

Linearized conservative finite element methods for the Nernst–Planck–Poisson equations

H Gao, D He - Journal of Scientific Computing, 2017‏ - Springer
The aim of this paper is to present and study new linearized conservative schemes with finite
element approximations for the Nernst–Planck–Poisson equations. For the linearized …

A positivity preserving and free energy dissipative difference scheme for the Poisson–Nernst–Planck system

D He, K Pan, X Yue - Journal of Scientific Computing, 2019‏ - Springer
In this paper, based on the reformulation of the Nernst–Planck equations, we construct an
unconditionally stable semi-implicit linearized difference scheme for the time dependent …

An unconditionally energy stable linear scheme for Poisson–Nernst–Planck equations

T Qiao, Z Qiao, S Sun, S Zhou - Journal of Computational and Applied …, 2024‏ - Elsevier
This paper proposes a linear, unconditionally energy-stable scheme for the Poisson–Nernst–
Planck (PNP) equations. Based on a gradient-flow formulation of the PNP equations, the …

Positivity-preserving third order DG schemes for Poisson–Nernst–Planck equations

H Liu, Z Wang, P Yin, H Yu - Journal of Computational Physics, 2022‏ - Elsevier
In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin
(DG) schemes for solving the time-dependent system of Poisson–Nernst–Planck (PNP) …

A dynamic mass transport method for Poisson-Nernst-Planck equations

H Liu, W Maimaitiyiming - Journal of Computational Physics, 2023‏ - Elsevier
A dynamic mass-transport method is proposed for approximately solving the Poisson–
Nernst–Planck (PNP) equations. The semi-discrete scheme based on the JKO type …