Bibliographic Details
| Title: |
Complexes from complexes: Finite element complexes in three dimensions. |
| Authors: |
Chen, Long1 (AUTHOR), Huang, Xuehai2 (AUTHOR) |
| Source: |
Mathematics of Computation. May2026, Vol. 95 Issue 359, p1083-1142. 60p. |
| Subjects: |
Finite element method, Mathematical complexes, Partial differential equations, Elasticity |
| Abstract: |
In the field of solving partial differential equations (PDEs), Hilbert complexes have become highly significant. Recent advances focus on creating new complexes using the Bernstein-Gelfand-Gelfand (BGG) framework, as shown by Arnold and Hu [Found. Comput. Math. 21 (2021), pp. 1739–1774]. This paper extends their approach to three-dimensional finite element complexes. The finite element Hessian, elasticity, and divdiv complexes are systematically derived by applying techniques such as smooth finite element de Rham complexes, the t-n decomposition, and trace complexes, along with related two-dimensional finite element analogs. The construction includes two reduction operations and one augmentation operation to address continuity differences in the BGG diagram, ultimately resulting in a comprehensive and effective framework for constructing finite element complexes, which have various applications in PDE solving. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
