A Family of curl-curl Conforming Finite Elements on Tetrahedral Meshes

Qian Zhang & Zhimin Zhang
2020 CSIAM Transactions on Applied Mathematics  
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
more » ... d-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.
doi:10.4208/csiam-am.2020-0023 fatcat:7hr3mevu65f4feb7bwxgkp7s54