论文标题
$ \ pmb {h}（\ mathrm {curl}）$ - 三维四维Quad-Curl问题的连续性
A new family of nonconforming elements with $\pmb{H}(\mathrm{curl})$-continuity for the three-dimensional quad-curl problem
论文作者
论文摘要
我们提出和分析了一个不合格的有限元素的新家庭，以解决三维四维折扣问题。提出的有限元元素空间是$ \ pmb {h}（\ mathrm {curl}）$的子空间，而不是$ \ pmb {h}（\ mathrm {grad}〜\ mathrm {curl {curl}）$，这与现有的不合格的$不同。证明了离散问题的充分性和最佳的错误估计，以离散$ \ pmb {h}（\ Mathrm {grad}〜\ Mathrm {curl}）$ norm，$ \ pmb {h}（\ pmb {h}）（\ \ mathrm {curl}）$ norm和$ \ pmb norm and $ \ pmb {l Norm der。提供数值实验来说明该方法的良好性能并确认我们的理论预测。
We propose and analyze a new family of nonconforming finite elements for the three-dimensional quad-curl problem. The proposed finite element spaces are subspaces of $\pmb{H}(\mathrm{curl})$, but not of $\pmb{H}(\mathrm{grad}~\mathrm{curl})$, which are different from the existing nonconforming ones. The well-posedness of the discrete problem is proved and optimal error estimates in discrete $\pmb{H}(\mathrm{grad}~\mathrm{curl})$ norm, $\pmb{H}(\mathrm{curl})$ norm and $\pmb{L}^2$ norm are derived. Numerical experiments are provided to illustrate the good performance of the method and confirm our theoretical predictions.
