TY - JOUR
T1 - A Family of Curl-Curl Conforming Finite Elements on Tetrahedral Meshes
AU - Zhang , Qian
AU - Zhang , Zhimin
JO - CSIAM Transactions on Applied Mathematics
VL - 4
SP - 639
EP - 663
PY - 2020
DA - 2020/12
SN - 1
DO - http://doi.org/10.4208/csiam-am.2020-0023
UR - https://global-sci.org/intro/article_detail/csiam-am/18540.html
KW - $H^2$(curl)-conforming, finite elements, tetrahedral mesh, quad-curl problems, interpolation errors, convergence analysis.
AB - <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>