Sponsor
This work was supported in part by the National Science Foundation (NSF) under grant DMS-2409900 (Jay Gopalakrishnan), DMS-2309606 (Johnny Guzman), and DMS-2110781 (Jeonghun J. Lee).
Published In
Journal of Numerical Mathematics
Document Type
Pre-Print
Publication Date
12-19-2025
Subjects
Johnson-Křížek-Mercier Elasticity Element, Stress, Superconvergence, Duality, Postprocessing.
Abstract
Mixed methods for linear elasticity with strongly symmetric stresses of lowest order are studied in this paper. On each simplex, the stress space has piecewise linear components with respect to its Alfeld split (which connects the vertices to barycenter), generalizing the Johnson–Mercier two-dimensional element to higher dimensions. Further reductions in the stress space in the three-dimensional case (to 24 degrees of freedom per tetrahedron) are possible when the displacement space is reduced to local rigid displacements. Proofs of optimal error estimates of numerical solutions and improved error estimates via postprocessing and the duality argument are presented.
Rights
© Copyright the author(s) 2025
DOI
10.1515/jnma-2025-0020
Persistent Identifier
https://archives.pdx.edu/ds/psu/44414
Publisher
Walter de Gruyter GmbH
Citation Details
Published as: Gopalakrishnan, J., Guzmán, J., & Lee, J. J. (2025). The Johnson–Křížek–Mercier elasticity element in higher dimensions. Journal of Numerical Mathematics.
Description
This is the author’s version of a work that was accepted for publication:
Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: (2025). The Johnson–Křížek–Mercier elasticity element in higher dimensions. Journal of Numerical Mathematics.