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

Qian Zhang; Lixiu Wang; Zhimin Zhang

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

Numerical Analysis 2018-05-09 v1

Authors: Qian Zhang , Lixiu Wang , Zhimin Zhang

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.

Keywords

h2(curl)-conforming finite element quad-curl problem finite element method convergence analysis numerical experiments

Cite

@article{arxiv.1805.02962,
  title  = {An $H^2$(curl)-conforming finite element in 2D and its applications to the quad-curl problem},
  author = {Qian Zhang and Lixiu Wang and Zhimin Zhang},
  journal= {arXiv preprint arXiv:1805.02962},
  year   = {2018}
}

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