Commuting diagrams for the TNT elements on cubes
Commuting diagrams for the TNT elements on cubes
复制标题
立方体上 TNT 元素的通勤图
DOI：
10.1090/s0025-5718-2013-02729-9
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
W. Qiu
中科院分区：
文献类型：
--
作者：
Bernardo Cockburn;W. Qiu
.我们提出了交换图的德拉姆复杂的新元素定义在立方体使用张量积空间。这些元素的显着特点是，与以前已知的结果形成鲜明对比，它们具有包含k次多项式的张量积空间的TiNiest空间，因此它们的缩写TNT。事实上，TNT元的局部空间与标准张量积空间的区别在于维数是一个与度k无关的小数目的空间。对于与发散算子相关联的空间，这样的数是7（立方体的顶点数减1），对于与旋度算子相关联的空间，这样的数是18（立方体的面数乘以面的顶点数减1），对于与梯度算子相关联的空间，这样的数是12（立方体的边数乘以边的顶点数减1）。
. We present commuting diagrams for the de Rham complex for new elements defined on cubes which use tensor product spaces. The distinctive feature of these elements is that, in sharp contrast with previously known results, they have the TiNiest spaces containing Tensor product spaces of polynomials of degree k , hence their acronym TNT. In fact, the local spaces of the TNT elements differ from the standard tensor product spaces by spaces whose dimension is a small number independent of the degree k . Such a number is 7 (the number of vertices of the cube minus one) for the space associated with the divergence operator, 18 (the number of faces of the cube times the number of vertices of a face minus one) for the space associated with the curl operator, and 12 (the number of edges of the cube times the number of vertices of an edge minus one) for the space associated with the gradient operator.
影响因子：
2.8
作者：
Cantwell, C. D.;Sherwin, S. J.;Kelly, P. H. J.
通讯作者：
Kelly, P. H. J.