SIAM Journal on Scientific Computing, Volume 42, Issue 6, Page A3859-A3877, January 2020.
We construct smooth finite element de Rham complexes in two space dimensions. This leads to three families of curl-curl-conforming finite elements, two of which contain two existing families. The simplest triangular and rectangular finite elements have only six and eight degrees of freedom, respectively. Numerical experiments for each family demonstrate the convergence and efficiency of the elements for solving the quad-curl problem.

中文翻译：

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二维中简单的符合卷曲要求的有限元

SIAM科学计算杂志，第42卷，第6期，第A3859-A3877页，2020年1月。
我们在两个空间维度上构造光滑的有限元de Rham复数。这导致了三类符合卷曲曲线的有限元，其中两个包含两个现有的族。最简单的三角形和矩形有限元分别只有六个和八个自由度。每个族的数值实验证明了解决四曲线问题的元素的收敛性和效率。