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Mathematics > Numerical Analysis

arXiv:1805.02962 (math)
[Submitted on 8 May 2018]

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

Authors: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.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1805.02962 [math.NA]
  (or arXiv:1805.02962v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1805.02962

Submission history

From: Qian Zhang [view email]
[v1] Tue, 8 May 2018 12:01:58 UTC (41 KB)
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