Trimmed serendipity finite element differential forms
Trimmed serendipity finite element differential forms
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DOI：
10.1090/mcom/3354
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发表时间：
2016-07
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影响因子：
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通讯作者：
A. Gillette;Tyler Kloefkorn
中科院分区：
文献类型：
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作者：
A. Gillette;Tyler Kloefkorn
我们介绍了家庭的修剪意外的有限元微分形式空间，定义在立方体网格在任何数量的维度，任何多项式的程度，并为任何形式的顺序。Arnold和Awanou [Math.Comp.83（288）2014]开发的修剪的偶然性族和（非修剪的）偶然性族之间的关系类似于来自有限元外演算的单纯网格上的修剪的和（非修剪的）多项式有限元微分形式族之间的关系。我们在一般情况下提供的自由度，并证明他们是unisolvent的修剪意外发现空间。具有固定多项式阶数r的修剪偶然空间序列提供了Christiansen和Gillette [ESAIM：M2 AN 50（3）2016]描述的系统的显式示例，即包含阶数r-1多项式微分形式的正方形或立方体上的最小相容有限元系统。
We introduce the family of trimmed serendipity finite element differential form spaces, defined on cubical meshes in any number of dimensions, for any polynomial degree, and for any form order. The relation between the trimmed serendipity family and the (non-trimmed) serendipity family developed by Arnold and Awanou [Math. Comp. 83(288) 2014] is analogous to the relation between the trimmed and (non-trimmed) polynomial finite element differential form families on simplicial meshes from finite element exterior calculus. We provide degrees of freedom in the general setting and prove that they are unisolvent for the trimmed serendipity spaces. The sequence of trimmed serendipity spaces with a fixed polynomial order r provides an explicit example of a system described by Christiansen and Gillette [ESAIM:M2AN 50(3) 2016], namely, a minimal compatible finite element system on squares or cubes containing order r-1 polynomial differential forms.