This paper discusses the construction of local bounded commuting projections for discrete subcomplexes of the gradgrad complexes in two and three dimensions, which play an important role in the finite element theory of elasticity (2D) and general relativity (3D). The construction first extends the local bounded commuting projections to the discrete de Rham complexes to other discrete complexes. Moreover, the argument also provides a guidance in the design of new discrete gradgrad complexes.

翻译：本文讨论二维和三维梯度梯度复形离散子复形的局部有界交换投影构造，这些复形在弹性力学（二维）和广义相对论（三维）的有限元理论中发挥重要作用。该构造首先将离散de Rham复形的局部有界交换投影扩展到其他离散复形，此外，这一论证也为设计新型离散梯度梯度复形提供了指导。