Analysis and Applied Mathematics Seminar: A uniformly hp-stable element for the elasticity complex, by Francis Aznaran
March 9, 2026
4:00 PM - 4:50 PM
Francis Aznaran (University of Notre Dame): A uniformly hp-stable element for the elasticity complex
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 HuZhang 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 BernsteinGelfandGelfand 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.
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Date posted
Mar 9, 2026
Date updated
Mar 9, 2026
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