2024/10/12 by Jun Hu, Rui Ma, Hu, Jun +3
Computer Science · Engineering · Mathematics · #65N30 #74B05 #Composite Structure Analysis and Optimization #Composite material #Contact Mechanics and Variational Inequalities #Economics #Elasticity (physics) #FOS: Mathematics #Finite element method #Linear elasticity #Materials science #Mathematical optimization #Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Order (exchange) #Physics #Thermodynamics
paper · pdf · doi:10.48550/arxiv.2410.09517
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/10/12 · openalex created_date 2024/10/20 · openalex updated_date 2026/07/28
In this paper, we construct two lower order mixed elements for the linear elasticity problem in the Hellinger-Reissner formulation, one for the 2D problem and one for the 3D problem, both on macro-element meshes. The discrete stress spaces enrich the analogous Pk stress spaces in [J. Hu and S. Zhang, arxiv, 2014, J. Hu and S. Zhang, Sci. China Math., 2015] with simple macro-element bubble functions, and the discrete displacement spaces are discontinuous piecewise Pk-1 polynomial spaces, with k=2,3, respectively. Discrete stability and optimal convergence is proved by using the macro-element technique. As a byproduct, the discrete stability and optimal convergence of the P2-P1 mixed element in [L. Chen and X. Huang, SIAM J. Numer. Anal., 2022] in 3D is proved on another macro-element mesh. For the mixed element in 2D, an H2-conforming composite element is constructed and an exact discrete elasticity sequence is presented. Numerical experiments confirm the theoretical results.