# A Two-grid Method for Linearizing and Symmetrizing the Steady-state Poisson-Nernst-Planck Equations

## TL;DR

This paper introduces a two-grid method that linearizes and symmetrizes the steady-state Poisson-Nernst-Planck equations, enhancing computational efficiency and providing error estimates with effective numerical results.

## Contribution

The paper presents a novel two-grid approach that improves efficiency in solving Poisson-Nernst-Planck equations by decoupling and linearizing the system, with proven error bounds.

## Key findings

- The two-grid method effectively linearizes and symmetrizes the equations.
- Numerical results confirm the method's efficiency and accuracy.
- Error estimates support the method's reliability.

## Abstract

In this paper, a two-grid method is proposed to linearize and symmetrize the steady-state Poisson-Nernst-Planck equations. The computational system is decoupled to linearize and symmetrize equations by using this method, which can improve the computational efficiency compared with the finite element method. Error estimates are derived for the proposed method. The numerical results show that the two-grid method is effective.