Numerical Studies for an Interface Problem Involving Fourth- and Second-Order Poisson-Fermi Electrostatic Equations
Year: 2025
Author: Mengjie Liu, Mingyan He, Pengtao Sun
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 2 : pp. 226–245
Abstract
A class of particular interface problems, which is derived from Bazant-Storey-Kornyshev (BSK) theory to account for the electrostatic correlation in concentrated electrolytes, is studied in this paper. It involves a modified fourth-order Poisson-Fermi equation in solvents and a second-order Poisson equation in solutes with high-contrast coefficients, where nonhomogeneous interface conditions are introduced over the interface that divides solutes from solvents. A type of interface-fitted finite element method is developed and analyzed for this interface problem, and optimal error estimates are obtained for all variables in both $H^1$ and $L^2$ norms. Numerical experiments validate all attained theoretical results through two mathematical examples, as well as the electrostatic correlation phenomenon in concentrated electrolytes through a physical example, practically, where the electrostatic stress and interactional forces in the concentrated electrolyte are computed to reveal the charge reversal phenomenon that is governed by the BSK theory.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1011
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 2 : pp. 226–245
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Fourth-/second-order Poisson-Fermi interface problem nonhomogeneous interface condition interface-fitted finite element method optimal convergence electrostatic correlation charge reversal.