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arXiv · 2411.10758

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

Shu Xu·Liqun Cao
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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.

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Shu Xu, Liqun Cao. 2024-11-16. Optimal convergence in finite element semi-discrete error analysis of the Doyle-Fuller-Newman model beyond 1D with a novel projection operator. https://doi.org/10.1093/imanum%2Fdraf065

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