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arXiv · 1805.02962

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

Qian Zhang·Lixiu Wang·Zhimin Zhang
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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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Qian Zhang, Lixiu Wang, Zhimin Zhang. 2018-05-08. An $H^2$(curl)-conforming finite element in 2D and its applications to the quad-curl problem. https://arxiv.org/abs/1805.02962

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