2024/09/25 by Francis R. A. Aznaran, Kaibo Hu, Aznaran, Francis R. A. +3 · 1 citation
Engineering · Physics and Astronomy · #65N30 #74B05 #74G15 #74S05 #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Mathematics #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2409.17414
openalex publication_date 2024/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the discretization of symmetric, divergence-conforming stress tensors in continuum mechanics, we prove inf-sup stability bounds which are uniform in polynomial degree and mesh size for the Hu--Zhang finite element in two dimensions. This is achieved via an explicit construction of a bounded right inverse of the divergence operator, with the crucial component being the construction of bounded Poincaré operators for the stress elasticity complex which are polynomial-preserving, in the Bernstein--Gelfand--Gelfand framework of the finite element exterior calculus. We also construct hp-bounded projection operators satisfying a commuting diagram property and hp-stable Hodge decompositions. Numerical examples are provided.