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Discrete tensor product BGG sequences: splines and finite elements (2302.02434v2)
Published 5 Feb 2023 in math.NA and cs.NA
Abstract: 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.