Discrete tensor product BGG sequences: Splines and finite elements

Bonizzoni, Francesca; Hu, Kaibo; Kanschat, Guido; Sap, Duygu

doi:10.1090/mcom/3969

Discrete tensor product BGG sequences: Splines and finite elements
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by Francesca Bonizzoni, Kaibo Hu, Guido Kanschat and Duygu Sap;

Math. Comp. 94 (2025), 517-549

DOI: https://doi.org/10.1090/mcom/3969

Published electronically: April 17, 2024

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Abstract:

In this paper, we provide a systematic discretization of the Bernstein-Gelfand-Gelfand diagrams and complexes over cubical meshes in 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 $\operatorname {div}\operatorname {div}$ complexes as examples for our construction.

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