Optimal convergence in finite element semi-discrete error analysis of the Doyle-Fuller-Newman model beyond 1D with a novel projection operator

TL;DR

This paper introduces a finite element semi-discrete error analysis for the Doyle-Fuller-Newman model of lithium-ion batteries in higher dimensions, utilizing a novel projection operator to achieve optimal convergence and extend applicability beyond isothermal conditions.

Contribution

It develops a new projection operator for multiscale equations, enabling optimal convergence analysis of the model in 2D and 3D, and provides the first numerical validation in this context.

Findings

Achieves optimal convergence rates of h + (Δr)^2.

Extends error analysis beyond isothermal conditions.

Provides numerical verification of theoretical results.

Abstract

We present a finite element semi-discrete error analysis for the Doyle-Fuller-Newman model, which is the most popular model for lithium-ion batteries. Central to our approach is a novel projection operator designed for the pseudo-($N$+1)-dimensional equation, offering a powerful tool for multiscale equation analysis. Our results bridge a gap in the analysis for dimensions $2 \le N \le 3$ and achieve optimal convergence rates of $h+(\Delta r)^2$. Additionally, we perform a detailed numerical verification, marking the first such validation in this context. By avoiding the change of variables, our error analysis can also be extended beyond isothermal conditions.