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Mathematics > Numerical Analysis

arXiv:2411.10758 (math)
[Submitted on 16 Nov 2024]

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

Authors: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.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2411.10758 [math.NA]
  (or arXiv:2411.10758v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2411.10758

Submission history

From: Shu Xu [view email]
[v1] Sat, 16 Nov 2024 09:27:45 UTC (1,502 KB)
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