论文标题
$ c^m $ - $ p_ {k}^{（3）} $和$ c^m $ - $ p_ {k}^{（4）} $在四面体和4D Simplicial Grid上的有限元素
The nodal basis of $C^m$-$P_{k}^{(3)}$ and $C^m$-$P_{k}^{(4)}$ finite elements on tetrahedral and 4D simplicial grids
论文作者
论文摘要
我们构建$ C^M $ - $ P_ {K}^{（3）} $（$ K \ ge 2^3M+1 $）和$ C^M $ -P_ {K}^{（4）} $（$ K \ ge 2^4M+1 $ 1 $）的鼻子基础。 $ c^m $ - $ p_ {k}^{（n）} $代表全球$ c^m $（$ m \ ge1 $）和本地分段$ n $ n $ d $ k $的$ n $ n $ d $ n $ dipermensional-Dipermensional-Dipermensional-demensial-demensial-demensial-demensial-demensial-demensial-demensial-Dimensial-demensial-demensial-demensial-demensial-demensial-demensial-Dipersicial Grids。我们证明了Uni-Solvency和构建的$ C^M $的$ C^M $连续性 - $ P_ {K}^{（3）} $和$ C^M $ - $ P_ {k}^{（4）} $有限元元素空间。提供了计算机代码，该计算机代码为$ c^m $ - $ p_k^{（n）} $有限元素的节点基础生成索引设置。
We construct the nodal basis of $C^m$-$P_{k}^{(3)}$ ($k \ge 2^3m+1$) and $C^m$-$P_{k}^{(4)}$ ($k \ge 2^4m+1$) finite elements on 3D tetrahedral and 4D simplicial grids, respectively. $C^m$-$P_{k}^{(n)}$ stands for the space of globally $C^m$ ($m\ge1$) and locally piecewise $n$-dimensional polynomials of degree $k$ on $n$-dimensional simplicial grids. We prove the uni-solvency and the $C^m$ continuity of the constructed $C^m$-$P_{k}^{(3)}$ and $C^m$-$P_{k}^{(4)}$ finite element spaces. A computer code is provided which generates the index set for the nodal basis of $C^m$-$P_k^{(n)}$ finite elements on $n$-dimensional simplicial grids.
