Commuting diagrams for the TNT elements on cubes (Q2871178)

The authors present the commuting diagrams for the de Rham complex for new elements defined on cubes with the use of tensor product spaces. The new elements contain the smallest spaces containing tensor product spaces of polynomials of degree \(k\), i.e. the tiniest tensor product space (TNT). The paper shows that the local spaces of the TNT elements differ from the standard tensor product spaces by a space with a small number independent of the degree \(k\). The spaces associated with the divergence operator, with the curl operator, and with the gradient operator are considered.