TY - JOUR
T1 - Numerical Studies for an Interface Problem Involving Fourth- and Second-Order Poisson-Fermi Electrostatic Equations
AU - Liu , Mengjie
AU - He , Mingyan
AU - Sun , Pengtao
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 226
EP - 245
PY - 2025
DA - 2025/02
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1011
UR - https://global-sci.org/intro/article_detail/ijnam/23822.html
KW - Fourth-/second-order Poisson-Fermi interface problem, nonhomogeneous interface
condition, interface-fitted finite element method, optimal convergence, electrostatic correlation, charge reversal.
AB - <p style="text-align: justify;">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.</p>