@Article{CSIAM-AM-1-4, author = {Zhang, Qian and Zhimin, Zhang}, 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 = {
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.
}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0023}, url = {https://global-sci.com/article/82390/a-family-of-curl-curl-conforming-finite-elements-on-tetrahedral-meshes} }