The Hu-Zhang element for linear elasticity on curved domains

2025/08/14 by Chen, Wei, Du, Xinyuan, Hu, Jun
#65N12 #65N30 #74S05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2508.10674

Abstract

This paper extends the Hu-Zhang element for linear elasticity to curved domains, preserving strong symmetry and H(div)-conformity. The non-polynomial structure of the curved Hu-Zhang element makes it difficult to analyze the stability, which is overcome by establishing a novel inf-sup condition. Optimal convergence rates are achieved for all variables except for the stress in the L²-norm. This suboptimality originates from the fact that the divergence space of the curved Hu-Zhang element is not contained in the discrete displacement space, which is improved by local p-enrichment on boundary elements. Two numerical experiments validate the theoretical results.

Citations

• A Reissner-Mindlin plate formulation using symmetric Hu-Zhang elements via polytopal transformations
• Higher order Bernstein-Bézier and Nédélec finite elements for the relaxed micromorphic model
• Divergence--free Scott--Vogelius elements on curved domains
• The Hellan-Herrmann-Johnson method with curved elements
• Fast Auxiliary Space Preconditioner for Linear Elasticity in Mixed Form
• Stabilized mixed finite element methods for linear elasticity on simplicial grids in ℝⁿ
• Finite element approximations of symmetric tensors on simplicial grids in Rn: the lower order case
• Finite element approximations of symmetric tensors on simplicial grids in Rn: the high order case
• A family of conforming mixed finite elements for linear elasticity on triangular grids
• A new family of efficient conforming mixed finite elements on both rectangular and cuboid meshes for linear elasticity in the symmetric formulation
• Two remarks on rectangular mixed finite elements for elasticity
• Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities
• Mixed finite elements for elasticity
• Optimal Finite-Element Interpolation on Curved Domains
• Optimal Isoparametric Finite Elements and Error Estimates for Domains Involving Curved Boundaries

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• Lower order mixed elements for the linear elasticity problem in 2D and 3D