Published In
ESAIM: Mathematical Modelling and Numerical Analysis
Document Type
Article
Publication Date
11-2023
Subjects
Elasticity sequences -- stress finite elements
Abstract
We construct conforming finite element elasticity complexes on Worsey–Farin splits in three dimensions. Spaces for displacement, strain, stress, and the load are connected in the elasticity complex through the differential operators representing deformation, incompatibility, and divergence. For each of these component spaces, a corresponding finite element space on Worsey–Farin meshes is exhibited. Unisolvent degrees of freedom are developed for these finite elements, which also yields commuting (cochain) projections on smooth functions. A distinctive feature of the spaces in these complexes is the lack of extrinsic supersmoothness at subsimplices of the mesh. Notably, the complex yields the first (strongly) symmetric stress finite element with no vertex or edge degrees of freedom in three dimensions. Moreover, the lowest order stress space uses only piecewise linear functions which is the lowest feasible polynomial degree for the stress space.
Rights
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Locate the Document
DOI
10.1051/m2an/2023084
Persistent Identifier
https://archives.pdx.edu/ds/psu/42682
Citation Details
Gong, S., Gopalakrishnan, J., Guzmán, J., & Neilan, M. (2023). Discrete elasticity exact sequences on Worsey–Farin splits. ESAIM: Mathematical Modelling and Numerical Analysis, 57(6), 3373-3402.