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

UR - http://www.scopus.com/inward/record.url?scp=84891794977&partnerID=8YFLogxK

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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 -