Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system

Convergent Finite Element Discretizations of the Navier-stokes-nernst-planck-poisson System

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...

Global Existence and Asymptotic Behavior of Self - Similar Solutions for the Navier - Stokes - Nernst - Planck - Poisson System in R 3

An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations

Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources, which describe the electrodiffusion of ions in a solvated biomolecular system. In this paper, some error bounds for a piecewise finite element approximation to this problem are derived. S...

Poisson-Boltzmann-Nernst-Planck model.

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 provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems,...

Error analysis of finite element method for Poisson-Nernst-Planck equations

In this paper we study the a priori error estimates of finite element method for the system of time-dependent Poisson–Nernst–Planck equations, and for the first time, we obtain its optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm,with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semia...