The Poisson–Nernst–Planck (PNP) model is based on a mean-field approximation of ion
interactions and continuum descriptions of concentration and electrostatic potential. It …

This work presents a few variational multiscale models for charge transport in complex
physical, chemical, and biological systems and engineering devices, such as fuel cells, solar …

In this work we design and analyze a free energy satisfying finite difference method for
solving Poisson–Nernst–Planck equations in a bounded domain. The algorithm is of second …

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 …

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 …

The molecular mechanism of ion channel gating and substrate modulation is elusive for
many voltage gated ion channels, such as eukaryotic sodium ones. The understanding of …

This review outlines the recent progress made in developing more accurate and efficient
solutions to model electrostatics in systems comprised of bio-macromolecules and …

In this paper, a linearized local conservative mixed finite element method is proposed and
analyzed for Poisson–Nernst–Planck (PNP) equations, where the mass fluxes and the …

This work extends our earlier two-domain formulation of a differential geometry based
multiscale paradigm into a multidomain theory, which endows us the ability to …

In this study, a linearized locally conservative scheme, based on using a weak Galerkin
(WG)-mixed finite element method (MFEM), is developed for the Poisson–Nernst–Planck …