In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where spatial adaptivity geometrical singularities and boundary layer effects are mainly considered. As a key contribution, equations studied systematically rigorous analysis residual-based posteriori error estimate of system is presented. With regularity linearized derive...

We propose and analyse two convergent fully discrete schemes to solve the incompressible Navier-Stokes-Nernst-Planck-Poisson system. The first scheme converges to weak solutions satisfying an energy and an entropy dissipation law. The second scheme uses Chorin’s projection method to obtain an efficient approximation that converges to strong solutions at optimal rates. Mathematics Subject Classi...

1 Architecture Department, Chang’an University, No. 161, Chang’an Road, Xi’an 710061, China 2 Architecture Department, Xi’an University of Architecture & Technology, No. 13, Yanta Road, Xi’an 710055, China 3 School of Remote Sensing and Information Engineering, Wuhan University, No. 129, Luoyu Road, Wuhan 430079, China 4 School of Internation Software, Wuhan University, No. 129, Luoyu Road, Wuh...

We propose an edge averaged finite element (EAFE) discretization to solve the Heat-PNP (Poisson-Nernst-Planck) equations approximately. Our method enforces positivity of computed charged density functions and temperature function. Also thermodynamic consistent discrete energy estimate which resembles second law system is prescribed. Numerical examples are provided.

Abstract Electrolyte-gated organic field-effect transistors (EGOFETs) represent a class of thin-film suited for sensing and biosensing in aqueous media, often at physiological conditions. The EGOFET device includes electrodes an semiconductor channel direct contact with electrolyte. Upon operation, electric double layers are formed along the gate-electrolyte channel-electrolyte interfaces, but ...

The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution o...

A quantum corrected Poisson-Nernst-Planck (QCPNP) model is proposed for simulating ionic currents through biological ion channels by taking into account both classical and quantummechanical effects. A generalized Gummel algorithm is also presented for solving the model system. Compared with the experimental results of X-ray crystallography, it is shown that the quantum PNP model is more accurat...

Electrochemical systems are considered for which the concentration of ions in solution is low, and therefore there is an electric field which extends deep into solution away from the electrode surface. Finite difference methods are used to model a potential step chronoamperometry experiment at a microhemisphere electrode. Concentration profiles, potential profiles, and current-time curves are p...