CSIAM Trans. Appl. Math., 1 (2020), pp. 639-663.
Published online: 2020-12
Cited by
- BibTex
- RIS
- TXT
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 = {http://global-sci.org/intro/article_detail/csiam-am/18540.html} }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.