Numerical analysis of a finite element formulation of the P2D model for Lithium-ion cells

TL;DR

This paper provides a rigorous numerical analysis of a finite element-implicit Euler scheme for the complex P2D model of lithium-ion batteries, including error estimates and solution existence and uniqueness.

Contribution

It introduces a detailed numerical analysis of the P2D model using finite element methods, which was not previously thoroughly studied.

Findings

Error estimates for semidiscrete and fully discrete systems

Proof of existence and uniqueness of solutions

Enhanced understanding of numerical stability for the P2D model

Abstract

The mathematical P2D model is a system of strongly coupled nonlinear parabolic-elliptic equations that describes the electrodynamics of lithium-ion batteries. In this paper, we present the numerical analysis of a finite element-implicit Euler scheme for such a model. We obtain error estimates for both the spatially semidiscrete and the fully discrete systems of equations, and establish the existence and uniqueness of the fully discrete solution.