Francis Aznaran : A uniformly hp-stable element for the elasticity complex

Posted by Gerard Awanou , part of the Analysis and Applied Mathematics Seminar.

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March 9, 2026, 4 p.m.

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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.