Work

The Johnson–Křížek–Mercier elasticity element in higher dimensions

Year: 2025

Type: article

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.

Source: Journal of Numerical Mathematics

DOI: 10.1515/jnma-2025-0020

Authors: Jay Gopalakrishnan, Johnny Guzmán, Jeonghun J. Lee

Institutions: Portland State University, Brown University, Baylor University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funder: National Science Foundation