H(curl$^2$)-Conforming Finite Elements in 2 Dimensions and Applications to the Quad-Curl Problem

Qian Zhang, Lixiu Wang, Zhimin Zhang
2019 SIAM Journal on Scientific Computing  
In this paper, we construct some H(curl 2 )-conforming finite elements on a rectangle (a parallelogram) and a triangle. The proposed elements possess some nice properties which have been proved by a rigorous theoretical analysis. Then we apply our new elements to construct a finite element space for discretizing the quad-curl problem. Convergence orders O(h k ) in the H(curl) norm and O(h k−1 ) in the H(curl 2 ) norm are established. Numerical experiments are provided to confirm the theoretical results.
doi:10.1137/18m1199988 fatcat:fgomzfvg6fcpjasd5egtmgvski