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

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.

This is the final version of the manuscript published in IMA Journal of Numerical Analysis. The published version is available at: https://doi.org/10.1093/imanum/draf065 Licensed under CC BY 4.0

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