论文标题
Brinkman的不合格有限元素和$ - \ text {curl}δ\ text {curl} $ Cubical Meshes上的问题
Nonconforming finite elements for the Brinkman and $-\text{curl}Δ\text{curl}$ problems on cubical meshes
论文作者
论文摘要
我们在立方网格上提出了两个不合格元素的家族：一个用于$ - \ text {curl}δ\ text {curl} $问题，另一个用于Brinkman问题。 $ - \ text {curl}δ\ text {curl} $问题的元素是立方网格上的第一个不合格元素。边缘人问题的元素可以产生相对于参数$ν$的均匀稳定有限元方法。 $ - \ text {curl}δ\ text {curl} $和Brinkman问题的最低级元素分别具有48和30度的自由度。 元素的两个家族是$ h（\ text {curl};ω）$和$ h（\ text {div};ω）$的子空间，而它们是不合格到$ h（\ text {gradcurl};ω）$和$ [h^1（ω）]^3 $的元素的不合格的近似值，并且可以与$ nipt $ nipt^$相同。
We propose two families of nonconforming elements on cubical meshes: one for the $-\text{curl}Δ\text{curl}$ problem and the other for the Brinkman problem. The element for the $-\text{curl}Δ\text{curl}$ problem is the first nonconforming element on cubical meshes. The element for the Brinkman problem can yield a uniformly stable finite element method with respect to the parameter $ν$. The lowest-order elements for the $-\text{curl}Δ\text{curl}$ and the Brinkman problems have 48 and 30 degrees of freedom, respectively. The two families of elements are subspaces of $H(\text{curl};Ω)$ and $H(\text{div};Ω)$, and they, as nonconforming approximation to $H(\text{gradcurl};Ω)$ and $[H^1(Ω)]^3$, can form a discrete Stokes complex together with the Lagrange element and the $L^2$ element.
