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 …

A second order accurate (in time) numerical scheme is proposed and analyzed for the
Poisson–Nernst–Planck equation (PNP) system, reformulated as a non-constant mobility H …

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 …

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 …

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 …

In this paper, we provide a theoretical analysis for an iteration solver to implement a finite
difference numerical scheme for the Poisson-Nernst–Planck (PNP) system, based on the …

A second order accurate (in time) numerical scheme is proposed and analyzed for the
Poisson-Nernst-Planck equation (PNP) system, reformulated as a non-constant mobility …

Ion transport, often described by the Poisson–Nernst–Planck (PNP) equations, is ubiquitous
in electrochemical devices and many biological processes of significance. In this work, we …

In this paper, we study a weak Galerkin (WG) finite element method for semiconductor
device simulations. We consider the one-dimensional drift–diffusion (DD) and high-field (HF) …

Ion transport plays a crucial role in biophysical and electrochemical applications. While
being modeled by the classical Poisson–Nernst–Planck (PNP) equations, many ionic …