Exact sequences on Worsey-Farin Splits
Exact sequences on Worsey-Farin Splits
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DOI：
10.1090/mcom/3746
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发表时间：
2020-08
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通讯作者：
J. Guzmán;A. Lischke;M. Neilan
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作者：
J. Guzmán;A. Lischke;M. Neilan
我们构造了定义在三维Worsey-Farin分裂上的几个光滑有限元空间。特别地，我们构造了C_1C^1，H_1(Curl)H^1(算子名{curl})和H_1H^1-协调有限元空间，并证明了离散空间满足局部精确度性质。空间的一个特征是它们的低多项式次数，并且在网格子简单处缺乏外部超光滑。在最低阶情形下，序列的最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-Stokes)方程的离散化。
We construct several smooth finite element spaces defined on three-dimensional Worsey–Farin splits. In particular, we construct C 1 C^1 , H 1 ( curl ) H^1(\operatorname {curl}) , and H 1 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 subsimplices 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.