2020/05/04 by Long Chen, Xuehai Huang, Chen, Long +1 · 5 citations
Engineering · #65N12 #65N15 #65N30 #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2005.01271
openalex publication_date 2020/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two types of finite element spaces on triangles are constructed for div-div conforming symmetric tensors. Besides the normal-normal continuity, the stress tensor is continuous at vertices and another trace involving combination of derivatives of stress is identified. Polynomial complex, finite element complex, and Hilbert complex are presented and a commuting diagram between them is given. The constructed div-div conforming elements are exploited to discretize the mixed formulation of the biharmonic equation. Optimal order and superconvergence error analysis is provided. By rotation, finite elements for rot-rot conforming symmetric strain are also obtained.