Title

Mixed Finite Element Method for Modified Poisson–Nernst–Planck/Navier–Stokes Equations

Document Type

Article

Publication Date

4-29-2021

Publication Title

Journal of Scientific Computing

Volume

87

Issue

3

First page number:

1

Last page number:

33

Abstract

In this paper, a complete mixed finite element method is developed for a modified Poisson–Nernst–Planck/Navier–Stokes (PNP/NS) coupling system, where the original Poisson equation in PNP system is replaced by a fourth-order elliptic equation to more precisely account for electrostatic correlations in a simplified form of the Landau–Ginzburg-type continuum model. A stabilized mixed weak form is defined for each equation of the modified PNP/NS model in terms of primary variables and their corresponding vector-valued gradient variables, based on which a stable Stokes-pair mixed finite element is thus able to be utilized to discretize all solutions to the entire modified PNP/NS model in the framework of Stokes-type mixed finite element approximation. Semi- and fully discrete mixed finite element schemes are developed and are analyzed for the presented modified PNP/NS equations, and optimal convergence rates in energy norms are obtained for both schemes. Numerical experiments are carried out to validate all attained theoretical results.

Keywords

A stabilized mixed finite element; Fourth-order elliptic equation; Modified Poisson–Nernst–Planck/Navier–Stokes (PNP/NS) coupling system; Optimal convergence; Taylor–Hood mixed element

Disciplines

Computer Sciences

Language

English

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