Misc,

An $H^2$(curl)-conforming finite element in 2D and its applications to the quad-curl problem

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(2018)cite arxiv:1805.02962.

Abstract

In this paper, we first construct the $H^2$(curl)-conforming finite elements both on a rectangle and a triangle. They possess some fascinating properties which have been proven by a rigorous theoretical analysis. Then we apply the elements to construct a finite element space for discretizing quad-curl problems. Convergence orders $O(h^k)$ in the $H$(curl) norm and $O(h^k-1)$ in the $H^2$(curl) norm are established. Numerical experiments are provided to confirm our theoretical results.

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