Analysis and Applied Mathematics Seminar
Francis Aznaran
University of Notre Dame
A uniformly hp-stable element for the elasticity complex
Abstract: For the discretisation 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.
Monday March 9, 2026 at 4:00 PM in 636 SEO