2025/08/02 by Xuehai Huang, Huang, Xuehai · 1 citation
Engineering · Materials Science · #58J10 #65N12 #65N30 #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #Nonlocal and gradient elasticity in micro/nano structures #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2508.01238
openalex publication_date 2025/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper extends the Bernstein-Gelfand-Gelfand (BGG) framework to the construction of finite element conformal Hessian complexes and conformal elasticity complexes in three dimensions involving conformal tensors (i.e., symmetric and traceless tensors). These complexes incorporate higher-order differential operators, including the linearized Cotton-York operator, and require conformal tensor spaces with nontrivial smoothness and trace conditions. A novel application of the discrete BGG framework, combined with the geometric decomposition of bubble spaces and a reduction operation, to local bubble finite element complexes is introduced. This yields simpler and more tractable constructions than global BGG-based approaches, and leads to the bubble conformal complexes. Building on these bubble conformal complexes and the associated face bubble complexes, finite element conformal Hessian complexes and conformal elasticity complexes with varying degrees of smoothness are systematically developed. The resulting complexes support stable and structure-preserving numerical methods for applications in relativity, Cosserat elasticity, and fluid mechanics.