Curl-curl conforming elements on tetrahedra
Numerical Analysis
2020-10-05 v2 Numerical Analysis
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.
Cite
@article{arxiv.2007.10421,
title = {Curl-curl conforming elements on tetrahedra},
author = {Qian Zhang and Zhimin Zhang},
journal= {arXiv preprint arXiv:2007.10421},
year = {2020}
}
Comments
6 figures;31 pages