Curl-curl conforming elements on tetrahedra release_7lmzlnzjc5dthnosrvbqvpkufu

by Qian Zhang, Zhimin Zhang

Released as a article .

2020  

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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Date   2020-10-01
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arXiv  2007.10421v2
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