Exact sequences在Worsey-Farin分裂上的应用
Exact sequences on Worsey-Farin Splits
摘要：
本文构造了几个定义在三维Worsey-Farin分裂上的光滑有限元空间。特别地，我们构造了$C^1$，$H^1(\curl)$和$H^1$ -协调有限元空间，并证明了这些离散空间满足局部正合性质.空间的一个特点是它们的低多项式次数和缺乏外在的超光滑次单形的网格。在最低阶情况下，序列中的后两个空间由分段线性空间和分段常数空间组成，适合于（Navier-）斯托克斯方程的离散化.
英文摘要：
We construct several smooth finite element spaces defined on three--dimensional Worsey--Farin splits. In particular, we construct $C^1$, $H^1(\curl)$, and $H^1$-conforming finite element spaces and show the discrete spaces satisfy local exactness properties. A feature of the spaces is their low polynomial degree and lack of extrinsic supersmoothness at sub-simplices of the mesh. In the lowest order case, the last two spaces in the sequence consist of piecewise linear and piecewise constant spaces, and are suitable for the discretization of the (Navier-)Stokes equation.
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