A new family of nonconforming elements with $\pmb{H}(\mathrm{curl})$-continuity for the three-dimensional quad-curl problem

Baiju Zhang; Zhimin Zhang

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arXiv · 2206.12056

A new family of nonconforming elements with $\pmb{H}(\mathrm{curl})$-continuity for the three-dimensional quad-curl problem

Baiju Zhang·Zhimin Zhang

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Abstract

We propose and analyze a new family of nonconforming finite elements for the three-dimensional quad-curl problem. The proposed finite element spaces are subspaces of $\pmb{H}(\mathrm{curl})$, but not of $\pmb{H}(\mathrm{grad}~\mathrm{curl})$, which are different from the existing nonconforming ones. The well-posedness of the discrete problem is proved and optimal error estimates in discrete $\pmb{H}(\mathrm{grad}~\mathrm{curl})$ norm, $\pmb{H}(\mathrm{curl})$ norm and $\pmb{L}^2$ norm are derived. Numerical experiments are provided to illustrate the good performance of the method and confirm our theoretical predictions.

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BibTeX RIS

Baiju Zhang, Zhimin Zhang. 2022-06-24. A new family of nonconforming elements with $\pmb{H}(\mathrm{curl})$-continuity for the three-dimensional quad-curl problem. https://arxiv.org/abs/2206.12056

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