An H²(curl)-conforming finite element in 2D and its applications to the quad-curl problem

2018/05/08 by Zhang, Qian, Wang, Lixiu, Zhang, Zhimin
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1805.02962

Abstract

In this paper, we first construct the H²(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 H²(curl) norm are established. Numerical experiments are provided to confirm our theoretical results.

Related

• Curl-curl conforming elements on tetrahedra
• Simple curl-curl-conforming finite elements in two dimensions
• A new family of nonconforming elements with \pmbH(curl)-continuity for the three-dimensional quad-curl problem
• H(curl²)-conforming quadrilateral spectral element method for quad-curl problems
• A priori and a posteriori error estimates for the quad-curl eigenvalue problem