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arXiv · 2007.10421

Curl-curl conforming elements on tetrahedra

Qian Zhang·Zhimin Zhang
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Abstract

In [24], we proposed H(curl^2)-conforming elements on both a triangle and a rectangle. This family of elements provides a brand new method to solve the quad-curl problem in 2 dimensions. In this paper, we turn our focus to 3 dimensions and construct an H(curl^2)-conforming tetrahedral finite element. The newly proposed element has been proved to have the optimal interpolation error estimate. Having tetrahedral elements, we can solve the quad-curl problem in any Lipschitz domain by conforming finite element method. We also provide several numerical examples of using our element to solve the quad-curl problem. The results of the numerical experiments show the effectiveness and correctness of our element.

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Qian Zhang, Zhimin Zhang. 2020-07-20. Curl-curl conforming elements on tetrahedra. https://arxiv.org/abs/2007.10421

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