TY - JOUR
T1 - Commuting diagrams for the tnt elements on cubes
AU - Cockburn, Bernardo
AU - Qiu, Weifeng
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Commuting diagrams
KW - Cubic element
KW - Tensor product spaces
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U2 - 10.1090/S0025-5718-2013-02729-9
DO - 10.1090/S0025-5718-2013-02729-9
M3 - Article
AN - SCOPUS:84891794977
SN - 0025-5718
VL - 83
SP - 603
EP - 633
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 286
ER -