Discrete tensor product BGG sequences: splines and finite elements
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866915350234267648 |
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| author | Bonizzoni, Francesca Hu, Kaibo Kanschat, Guido Sap, Duygu |
| author_facet | Bonizzoni, Francesca Hu, Kaibo Kanschat, Guido Sap, Duygu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02434 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Discrete tensor product BGG sequences: splines and finite elements Bonizzoni, Francesca Hu, Kaibo Kanschat, Guido Sap, Duygu Numerical Analysis 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. |
| title | Discrete tensor product BGG sequences: splines and finite elements |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2302.02434 |