%0 Generic %1 zhang2018h2curlconforming %A Zhang, Qian %A Wang, Lixiu %A Zhang, Zhimin %D 2018 %K 65n12-pdes-bvps-stability-and-convergence-of-numerical-methods65n15-pdes-bvps-error-bounds65n30-pdes-bvps-finite-elements35q60-pdes-in-connection-with-optics-and-electromagnetic-theory35b45-pdes-a-priori-estimates %T An $H^2$(curl)-conforming finite element in 2D and its applications to the quad-curl problem %U http://arxiv.org/abs/1805.02962 %X 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.

@misc{zhang2018h2curlconforming, 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.}, added-at = {2022-02-17T06:38:28.000+0100}, author = {Zhang, Qian and Wang, Lixiu and Zhang, Zhimin}, biburl = {https://www.bibsonomy.org/bibtex/277a0edef11480e43418d98f30b7392b9/gdmcbain}, interhash = {9349c2b0aa2836895c87aa3ef8245c39}, intrahash = {77a0edef11480e43418d98f30b7392b9}, keywords = {65n12-pdes-bvps-stability-and-convergence-of-numerical-methods65n15-pdes-bvps-error-bounds65n30-pdes-bvps-finite-elements35q60-pdes-in-connection-with-optics-and-electromagnetic-theory35b45-pdes-a-priori-estimates}, note = {cite arxiv:1805.02962}, timestamp = {2022-02-17T06:38:28.000+0100}, title = {An $H^2$(curl)-conforming finite element in 2D and its applications to the quad-curl problem}, url = {http://arxiv.org/abs/1805.02962}, year = 2018 }