In this paper, we provide a systematic discretization of the Bernstein-Gelfand-Gelfand (BGG) diagrams and complexes over cubical meshes of arbitrary dimension via the use of tensor-product structures of one-dimensional piecewise-polynomial spaces, such as spline and finite element spaces. We demonstrate the construction of the Hessian, the elasticity, and the divdiv complexes as examples for our construction.

翻译：本文通过使用一维分段多项式空间（如样条空间和有限元空间）的张量积结构，提供了任意维度立方体网格上Bernstein-Gelfand-Gelfand（BGG）图与复形的系统离散化方法。我们以黑塞、弹性及divdiv复形为例，展示了该构造过程。