Discrete tensor product BGG sequences: splines and finite elements

02/05/2023

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by   Francesca Bonizzoni, et al.

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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 ÷÷ complexes as examples for our construction.