Starting from the well-understood de Rham complex, it is possible to derive new complexes and deduce their properties from those of the starting complex. This construction is related to the Bernstein-Gelfand-Gelfand (BGG) sequence.
In this talk, we provide a systematic discretization of the Bernstein-Gelfand-Gelfand diagrams and complexes over Cartesian meshes in arbitrary dimension via the use of tensor product structures of one-dimensional piecewise-polynomial spaces, such as spline and finite element spaces.