@Article{CSIAM-AM-1-639,
author = {Zhang , Qian and Zhang , Zhimin},
title = {A Family of Curl-Curl Conforming Finite Elements on Tetrahedral Meshes},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2020},
volume = {1},
number = {4},
pages = {639--663},
abstract = {<p style="text-align: justify;">In [23], we, together with our collaborator, proposed a family of $H$(curl$^2$)-
conforming elements on both triangular and rectangular meshes. The elements provide 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 $H$(curl$^2$)-conforming finite
elements on tetrahedral meshes. The newly proposed elements have been proved to
have the optimal interpolation error estimate. Having the tetrahedral elements, we can
solve the quad-curl problem in any Lipschitz domain by the conforming finite element
method. We also provide several numerical examples of using our elements to solve
the quad-curl problem. The results of the numerical experiments show the correctness
of our elements.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.2020-0023},
url = {http://global-sci.org/intro/article_detail/csiam-am/18540.html}
}