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 …

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 …

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 …

In this work, we consider numerical methods for the Poisson–Nernst–Planck–Cahn–Hilliard
(PNPCH) equations with steric interactions, which correspond to a non-constant mobility H …

In this article, we propose and analyze a fully coupled, nonlinear, and energy-stable virtual
element method (VEM) for solving the coupled Poisson–Nernst–Planck (PNP) and Navier …

To study ion transport in electrolyte solutions, we propose numerical methods for a modified
Poisson–Nernst–Planck model with ionic steric effects (SPNP). Positivity preserving …

Charge dynamics play essential role in many practical applications such as semiconductors,
electrochemical devices and transmembrane ion channels. A Maxwell-Ampère Nernst …

Ion transport, involving the diffusion and migration of ions within the electrolyte, stands as a
fundamental concept in electrochemistry and serves as the driving force for electrochemical …

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 …

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 …