Unconditional stability and error estimates of FEMs for the electro-osmotic flow in micro-channels

TL;DR

This paper develops an unconditionally stable finite element method with optimal error estimates for simulating electro-osmotic flow in micro-channels, validated through numerical experiments.

Contribution

It introduces a new finite element scheme with proven stability and convergence for electro-osmotic flow modeling in micro-channels.

Findings

The method is unconditionally stable.

Achieves optimal convergence rates.

Effectively simulates electro-osmotic flows in complex micro-channels.

Abstract

In this paper, we will provide the the finite element method for the electro-osmotic flow in micro-channels, in which a convection-diffusion type equation is given for the charge density $\rho^e$. A time-discrete method based on the backward Euler method is designed. The theoretical analysis shows that the numerical algorithm is unconditionally stable and has optimal convergence rates. To show the effectiveness of the proposed model, some numerical results for the electro-osmotic flow in the T-junction micro-channels and in rough micro-channels are provided. Numerical results indicate that the proposed numerical method is suitable for simulating electro-osmotic flows.